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Triangles Diagonal Fibonacci
Triangles having the Fibonacci sequence as a diagonal or column
A010048 0 SC Triangle of Fibonomial coefficients.
A010048 0 SD Triangle of Fibonomial coefficients.
A011794 0 LD Triangle defined by a(n+1,k)=a(n,k-1)+a(n-1,k), a(n,1)=1, a(1,k)=1, a(2,k)=min(2,k).
A016095 0 FC Triangular array T(n,k) read by rows, where T(n,k) = coefficient of x^n*y^k in 1/(1-x-y-(x+y)^2).
A016095 0 LD Triangular array T(n,k) read by rows, where T(n,k) = coefficient of x^n*y^k in 1/(1-x-y-(x+y)^2).
A017125 0 FC Table read by antidiagonals of Fibonacci-type sequences.
A017125 0 SC Table read by antidiagonals of Fibonacci-type sequences.
A028412 0 LD Rectangular array of numbers Fibonacci(m(n+1))/Fibonacci(m), m>=1, n>=0, read by antidiagonals.
A035506 0 FC Stolarsky array read by antidiagonals.
A035513 0 FC Wythoff array read by antidiagonals.
A036355 0 FC Fibonacci-Pascal triangle read by rows.
A036355 0 LD Fibonacci-Pascal triangle read by rows.
A037027 0 FC Skew Fibonacci-Pascal triangle read by rows.
A038137 0 LD Reflection of A037027: T(n,m) = U(n,n-m), m=0..n, where U is as in A037027.
A039913 0 FC Triangular "Fibonacci array".
A039913 0 LD Triangular "Fibonacci array".
A039913 0 SC Triangular "Fibonacci array".
A039913 0 SD Triangular "Fibonacci array".
A045995 0 SC Rows of Fibonacci-Pascal triangle.
A045995 0 SD Rows of Fibonacci-Pascal triangle.
A046741 0 LD Triangle read by rows giving number of arrangements of k dumbbells on 2 X n grid (n >= 0, k >= 0).
A048887 0 SD Array T read by antidiagonals, where T(m,n) = number of compositions of n into parts <= m.
A050446 0 SC Table T(n,m) giving total degree of n-th-order elementary symmetric polynomials in m variables, -1 <= n, 1 <= m, read by antidiagonals.
A050447 0 SD Table T(n,m) giving total degree of n-th-order elementary symmetric polynomials in m variables, -1 <= n, 1 <= m, transposed and read by antidiagonals.
A050609 0 LD Table T(n,k) = Sum_{i=0..2n} (C(2n,i) mod 2)*F(i+k) = Sum_{i=0..n} (C(n,i) mod 2)*F(2i+k).
A050610 0 FC Sum_{i=0..y} (C(y,i) mod 2)*F(2i+x) = FL(y+x)*A050613[y], where A050613[y] = Product(L(2^i)^bit(y,i),i=0..[log2(y+1)]).
A053538 0 FC Triangle: a(n,m) = ways to place p balls in n slots with m in the rightmost p slots, 0<=p<=n, 0<=m<=n, summed over p, a(n,m)= Sum[binomial[k,m]binomial[n-k,k-m],{k,0,n} ], (see program line).
A054450 0 FC Triangle of partial row sums of unsigned triangle A049310(n,m), n >= m >= 0 (Chebyshev S-polynomials).
A055830 0 FC Triangle T read by rows: diagonal differences of triangle A037027.
A055870 0 SC Signed Fibonomial triangle.
A055870 0 SD Signed Fibonomial triangle.
A058071 0 FC A Fibonacci triangle: triangle T(n,k) in which n-th row consists of the numbers F(k)F(n+2-k), where F() are the Fibonacci numbers, for n >= 0, 0<=k<=n+1.
A058071 0 LD A Fibonacci triangle: triangle T(n,k) in which n-th row consists of the numbers F(k)F(n+2-k), where F() are the Fibonacci numbers, for n >= 0, 0<=k<=n+1.
A058071 0 SC A Fibonacci triangle: triangle T(n,k) in which n-th row consists of the numbers F(k)F(n+2-k), where F() are the Fibonacci numbers, for n >= 0, 0<=k<=n+1.
A058071 0 SD A Fibonacci triangle: triangle T(n,k) in which n-th row consists of the numbers F(k)F(n+2-k), where F() are the Fibonacci numbers, for n >= 0, 0<=k<=n+1.
A059389 0 FC Sums of two nonzero Fibonacci numbers.
A059779 0 SC A Lucas triangle: T(m,n), m >= n >= 0.
A059779 0 SD A Lucas triangle: T(m,n), m >= n >= 0.
A060959 0 SC Table by antidiagonals of generalized Fibonacci numbers: T(n,k)=T(n,k-1)+n*T(n,k-2) with T(n,0)=0 and T(n,1)=1.
A061451 0 LD Array T(n,k) of k-th order Fibonacci numbers read by antidiagonals in up-direction.
A063967 0 FC Triangle with a(n,k) = a(n-1,k) + a(n-2,k) + a(n-1,k-1) + a(n-2,k-1) and a(0,0) = 1.
A067330 0 FC Triangle read by rows of incomplete convolutions of Fibonacci numbers F(n+1) = A000045(n+1), n>=0.
A067330 0 SC Triangle read by rows of incomplete convolutions of Fibonacci numbers F(n+1) = A000045(n+1), n>=0.
A067418 0 LD Triangle A067330 with rows read backwards.
A067418 0 SD Triangle A067330 with rows read backwards.
A073133 0 LD Table by antidiagonals of T(n,k) = n*T(n,k-1) + T(n,k-2) starting with T(n,1) = 1.
A073450 0 LD Triangle T(j,k) = remainder of Fibonacci(j) divided by Fibonacci(k), for 3 < j and 2 < k < j.
A073450 0 SD Triangle T(j,k) = remainder of Fibonacci(j) divided by Fibonacci(k), for 3 < j and 2 < k < j.
A074829 0 FC Triangle formed by Pascal's rule, except begin and end the n-th row with the n-th Fibonacci number.
A074829 0 LD Triangle formed by Pascal's rule, except begin and end the n-th row with the n-th Fibonacci number.
A075148 0 LD Table E(n,k) (listed antidiagonalwise as E(0,0), E(1,0), E(0,1), E(2,0), E(1,1), E(0,2), ...) where E(n,k) is F(n+k) for all even n and L(n+k) for all odd n. F(n) and L(n) are the n-th Fibonacci (A000045) and Lucas (A000032) numbers respectively.
A076791 0 SC Triangle a(n,k) giving number of binary sequences of length n containing k subsequences 00.
A080018 0 LD Triangle of coefficients of polynomials P(n; x) = Permanent(M), where M=[m(i,j)] is n X n matrix defined by m(i,j)=x if -1<=i-j<=1 else m(i,j)=1.
A081572 0 LD Square array of binomial transforms of Fibonacci numbers, read by antidiagonals.
A081576 0 LD Square array of binomial transforms of Fibonacci numbers, read by antidiagonals.
A083412 0 LD Wythoff array read by antidiagonals.
A083856 0 SD Square array of generalized Fibonacci numbers, read by antidiagonals.
A085143 0 SD Triangle table from number wall of reversion of Fibonacci numbers.
A089107 0 LD Square array T(r,j) (r>=1, j>=1) read by antidiagonals, where T(r,j) is the convoluted convolved Fibonacci number G_j^(r) (see the Moree paper).
A089112 0 LD Square array T(r,j) (r>=1, j>=1) read by antidiagonals, where T(r,j) is the sign twisted convoluted convolved Fibonacci number H_j^(r) (see the Moree paper).
A089934 0 FC Table T(n,k) of the number of n X k matrices on {0,1} without adjacent 0's in any row or column.
A089934 0 LD Table T(n,k) of the number of n X k matrices on {0,1} without adjacent 0's in any row or column.
A089980 0 SC Array read by antidiagonals: T(n,m) = number of independent sets in the grid graph P_n x P_m.
A089980 0 SD Array read by antidiagonals: T(n,m) = number of independent sets in the grid graph P_n x P_m.
A090888 0 LD Matrix defined by a(n,k) = 3^n*Fibonacci(k) - 2^n*Fibonacci(k-2), read by antidiagonals.
A091533 0 FC Triangle read by rows, related to Pascal's triangle.
A091533 0 LD Triangle read by rows, related to Pascal's triangle.
A091562 0 FC Triangle read by rows, related to Pascal's triangle.
A091562 0 LD Triangle read by rows, related to Pascal's triangle.
A091594 0 FC Triangle read by rows: T(n,m) := sum{k=0..floor((n-m)/2), binomial(n-2k,m)binomial(n-m-k,k)}.
A092921 0 SC Array F(k,n) read by antidiagonals: k-generalized Fibonacci numbers.
A094067 0 LD Triangle read by rows: T(n,k) is the number of permutations p of [n] in which the length of the longest initial segment avoiding the 123-, the 132- and the 321-pattern is equal to k.
A094435 0 LD Triangular array read by rows: T(n,k)=F(k)C(n,k), k=1,2,3,...,n; n>=1.
A094436 0 LD Triangular array T(n,k) = F(k+1)C(n,k), k=0,1,2,3,...,n; n>=0.
A094437 0 LD Triangular array T(n,k)=F(k+2)C(n,k), k=0,1,2,3,...,n; n>=0.
A094438 0 LD Triangular array T(n,k)=F(k+3)C(n,k), k=0,1,2,3,...,n; n>=0.
A094439 0 LD Triangular array T(n,k)=F(k+4)C(n,k), k=0,1,2,3,...,n; n>=0.
A094440 0 FC Triangular array T(n,k) = F(n+1-k)*C(n,k-1), k = 1,2,3,...,n; n >= 1.
A094441 0 FC Triangular array T(n,k)=F(n+1-k)C(n,k), 0<=k<=n.
A094442 0 FC Triangular array T(n,k)=F(n+2-k)C(n,k), 0<=k<=n.
A094443 0 FC Triangular array T(n,k)=F(n+3-k)C(n,k), k=0,1,2,...,n; n>=0.
A094444 0 FC Triangular array T(n,k)=F(n+4-k)C(n,k), k=0,1,2,...,n; n>=0.
A094570 0 FC Triangle T(n,k) read by rows: T(n,k) = F(k) + F(n-k) where F(n) is the n-th Fibonacci number.
A094570 0 LD Triangle T(n,k) read by rows: T(n,k) = F(k) + F(n-k) where F(n) is the n-th Fibonacci number.
A094585 0 FC Triangle T of all positive differences of distinct Fibonacci numbers; also, triangle of all sums of consecutive distinct Fibonacci numbers.
A094585 0 SC Triangle T of all positive differences of distinct Fibonacci numbers; also, triangle of all sums of consecutive distinct Fibonacci numbers.
A094608 0 FC Rectangular array T by antidiagonals: row n consists of ranks of n in A000119.
A096669 0 SC Rectangular array T(n,k) read by antidiagonals; generating function of row n is 1/F(n,x), where F(n,x) is the polynomial 1 - x - x^2 - 2*x^3 -...- F(n+1)*x^n and F(n+1) is the (n+1)st Fibonacci number, for n=0,1,2,...
A096670 0 SD Rectangular array T(n,k) read by antidiagonals; generating function of column n is 1/F(n,x), where F(n,x) is the polynomial 1 - x - x^2 - 2*x^3 -...- F(n+1)*x^n and F(n+1) is the (n+1)st Fibonacci number, for n=0,1,2,...
A097351 0 FC Rectangular array T(n,k) by antidiagonals; rows are generalized Fibonacci sequences and every relatively prime pair (i,j) satisfying 1 <= i < j occurs exactly once.
A097352 0 FC Rectangular array T(n,k) by antidiagonals; rows are generalized Fibonacci sequences and every pair (i,j) satisfying 1 <= i < j occurs exactly once.
A098356 0 SC Multiplication table of the Fibonacci numbers read by antidiagonals.
A098356 0 SD Multiplication table of the Fibonacci numbers read by antidiagonals.
A098805 0 FC Array read by antidiagonals: Numerical sequences of Fibonacci-like polynomials produced by m-ary Huffman trees of maximum height for absolutely ordered sequences.
A098824 0 FC Array read by antidiagonals: Minimizing absolutely ordered sequences of m-ary Huffman trees of maximum height; m > 1.
A099233 0 SD Square array read by anti-diagonals associated to sections of 1/(1-x-x^k).
A099238 0 SD Square array read by anti-diagonals with rows generated by 1/(1-x-x^(k+1)).
A099390 0 SC Array T(m,n) read by antidiagonals: number of domino tilings (or dimer tilings) of the m X n grid (or m X n rectangle), for m>=1, n>=1.
A099390 0 SD Array T(m,n) read by antidiagonals: number of domino tilings (or dimer tilings) of the m X n grid (or m X n rectangle), for m>=1, n>=1.
A099573 0 LD Reverse of number triangle A054450.
A100578 0 SC Table read by rows: T(n,k) = if n<=k then n else Sum(T(n-i,k):1<=i<=k), 1<=k<=n, triangle read by rows.
A102310 0 FC Square array read by antidiagonals: Fib(k*n).
A102310 0 LD Square array read by antidiagonals: Fib(k*n).
A102756 0 LD Triangle T(n,k), 0<=k<=n, read by rows defined by: T(n,k) = T(n-1,k-1) + 2*T(n-1,k) + T(n-2,k-2) - T(n-2,k), T(0,0) = 1, T(n,k) = 0 if k < 0 or if n < k.
A103323 0 LD Square array T(n,k) read by antidiagonals: powers of Fibonacci numbers.
A103610 0 SD 4 X infinity array read by rows: let M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 1, 0}}, w[0] = {0, 0, 1, 1}', w[n]' = M*w[n -1]'; the n-th row of the array is w[n]' (the prime denotes transpose).
A103910 0 SD Triangle T read by rows: inverse of fibonomial triangle (A010048).
A104726 0 FC Triangle generated as the matrix product of A026729 and A000012 (triangular views), read by rows.
A104726 0 SC Triangle generated as the matrix product of A026729 and A000012 (triangular views), read by rows.
A104733 0 LD Triangle T(n,k) = sum_{j=k..n} Fibonacci(n-j+1)*Fibonacci(k+1), read by rows, 0<=k<=n.
A104762 0 FC Triangle read by rows: row n contains first n nonzero Fibonacci numbers in decreasing order.
A104762 0 SC Triangle read by rows: row n contains first n nonzero Fibonacci numbers in decreasing order.
A104763 0 LD Triangle read by rows: Fibonacci(1), Fibonacci(2),..,Fibonacci(n) in row n.
A104763 0 SD Triangle read by rows: Fibonacci(1), Fibonacci(2),..,Fibonacci(n) in row n.
A105422 0 FC Triangle read by rows: T(n,k) is the number of compositions of n having exactly k parts equal to 1.
A105809 0 FC A Fibonacci-Pascal matrix.
A106196 0 FC Triangle read by rows, generated from Pascal's triangle.
A106198 0 FC Triangle, columns = successive binomial transforms of Fibonacci numbers.
A106408 0 FC Triangle, read by rows, where T(1,1) = 1; T(2,1) = T(2,2) = 2; for n>2 T(n,n) = T(n-1,n-1) + T(n-2,n-2); T(n+1,n) = 2 * T(n,n); for all other entries T(n,k) = T(n-1,k) + T(n-2,k).
A106408 0 LD Triangle, read by rows, where T(1,1) = 1; T(2,1) = T(2,2) = 2; for n>2 T(n,n) = T(n-1,n-1) + T(n-2,n-2); T(n+1,n) = 2 * T(n,n); for all other entries T(n,k) = T(n-1,k) + T(n-2,k).
A106740 0 LD Triangle read by rows: greatest common divisors of pairs of Fibonacci numbers greater than 1: T(n,k) = GCD(Fib(n),Fib(k)), 2<k<n.
A108035 0 FC Triangle read by rows: n-th row is n-th nonzero Fibonacci number repeated n times.
A108035 0 LD Triangle read by rows: n-th row is n-th nonzero Fibonacci number repeated n times.
A108035 0 SC Triangle read by rows: n-th row is n-th nonzero Fibonacci number repeated n times.
A108035 0 SD Triangle read by rows: n-th row is n-th nonzero Fibonacci number repeated n times.
A108036 0 SC Triangle read by rows: the triangle in A108035 surrounded by a border of 0's.
A108036 0 SD Triangle read by rows: the triangle in A108035 surrounded by a border of 0's.
A108037 0 FC Triangle read by rows: n-th row is n-th nonzero Fibonacci number repeated n+1 times.
A108037 0 LD Triangle read by rows: n-th row is n-th nonzero Fibonacci number repeated n+1 times.
A108037 0 SC Triangle read by rows: n-th row is n-th nonzero Fibonacci number repeated n+1 times.
A108037 0 SD Triangle read by rows: n-th row is n-th nonzero Fibonacci number repeated n+1 times.
A108038 0 FC Triangle read by rows: g.f. = (x+y+x*y)/((1-x-x^2)*(1-y-y^2)).
A108038 0 LD Triangle read by rows: g.f. = (x+y+x*y)/((1-x-x^2)*(1-y-y^2)).
A108617 0 FC Triangle read by rows: T(n,k) = T(n-1,k-1)+T(n-1,k) for 0<k<n, T(n,0) = T(n,n) = n-th Fibonacci number.
A108617 0 LD Triangle read by rows: T(n,k) = T(n-1,k-1)+T(n-1,k) for 0<k<n, T(n,0) = T(n,n) = n-th Fibonacci number.
A108617 0 SC Triangle read by rows: T(n,k) = T(n-1,k-1)+T(n-1,k) for 0<k<n, T(n,0) = T(n,n) = n-th Fibonacci number.
A108617 0 SD Triangle read by rows: T(n,k) = T(n-1,k-1)+T(n-1,k) for 0<k<n, T(n,0) = T(n,n) = n-th Fibonacci number.
A109754 0 LD Matrix defined by: a(i,0) = 0, a(i,j) = i*Fibonacci[j-1] + Fibonacci[j], for j > 0; read by antidiagonals.
A109754 0 SD Matrix defined by: a(i,0) = 0, a(i,j) = i*Fibonacci[j-1] + Fibonacci[j], for j > 0; read by antidiagonals.
A109906 0 FC A triangle of coefficients based on A000045 and the Pascal's triangle: t(n,m)=Fibonacci[(n - m + 1)]*Fibonacci[(m + 1)]*Binomial[n, m].
A109906 0 LD A triangle of coefficients based on A000045 and the Pascal's triangle: t(n,m)=Fibonacci[(n - m + 1)]*Fibonacci[(m + 1)]*Binomial[n, m].
A110541 0 SC A number triangle of sums of binomial products.
A111006 0 LD Another version of Fibonacci-Pascal triangle A037027.
A111946 0 LD Triangle read by rows: T(n,k) = gcd(Fibonacci(n), Fibonacci(k)), 1 <= k <= n.
A112973 0 FC Riordan array (1/(1-x-x^2), x(1+x)/(1-x-x^2)^2).
A113020 0 LD Number triangle whose row sums are the Fibonacci numbers.
A114597 0 LD Triangle read by rows: T(n,k) is the number of hill-free Dyck paths of semilength n having pyramid weight k.
A116183 0 LD Array T(k,n) = number of meaningful differential operations of the n-th order on the space R^(3+k), for k=>0, n>0, read by antidiagonals.
A117501 0 LD Triangle generated from an array of generalized Fibonacci-like terms.
A117501 0 SD Triangle generated from an array of generalized Fibonacci-like terms.
A117502 0 LD Triangle, row sums = A001595.
A117502 0 SD Triangle, row sums = A001595.
A117715 0 SC Triangle T(n,m) containing the value of the Fibonacci polynomial F(n,x) at x=m.
A117915 0 LD Generalized Fibonacci-like triangle.
A117915 0 SD Generalized Fibonacci-like triangle.
A118654 0 LD Matrix, a(n,k) = 2^n*Fibonacci(k) - Fibonacci(k-2), read by anti-diagonals.
A118654 0 SD Matrix, a(n,k) = 2^n*Fibonacci(k) - Fibonacci(k-2), read by anti-diagonals.
A119011 0 FC Triangle read by rows: T(n,k) is the number of hill-free Dyck paths of semilength n and having k valleys strictly above the x-axis (0<=k<=n-2; n>=2). A hill in a Dyck path is a peak at level 1.
A119444 0 LD Triangle as described in A100461, except with a(1,n) = the Fibonacci numbers 1,2,3,5,8,... instead of 2^(n-1).
A119457 0 LD Triangle read by rows: T(n,1)=n, T(n,2)=(n-1)*2 for n>1 and T(n,k)=T(n-1,k-1)+T(n-2,k-2) for 2<k<=n.
A121875 0 FC Triangular array read by rows: see Comments for definition.
A122070 0 FC Triangle T(n,k), 0<=k<=n, given by T(n,k)=Fibonacci(n+k+1)*binomial(n,k).
A122075 0 FC Coefficients of a generalized Pell-Lucas polynomial read by rows.
A122837 0 FC Triangle T(n,k), 0<=k<=n, defined by : T(n,k)=0 if k<0, T(n,k)=0 if k>n,T(0,0)=1, T(1,0)=1, T(1,1)=-1, T(n,k)=T(n-1,k-1)+T(n-1,k)+T(n-2,k).
A122950 0 LD Triangle T(n,k), 0<=k<=n, read by rows, given by [0, 0, 1, -1, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 1, -1, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938.
A123262 0 LD Fibonacci-tribonacci triangle.
A123585 0 LD Triangle T(n,k), 0<=k<=n, given by [1, -1, 1, 0, 0, 0, 0, 0, ...] DELTA [1, 1, -1, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938.
A124031 0 FC Alternating sign center tridiagonal matrices as triangular sequences: m(n,m,d)=If[ n == m, (-1)^n, If[n == m - 1 || n == m + 1, -1, 0]].
A124032 0 FC Triangle read by rows: T(n,k) is the coefficient of x^k in the polynomial p(n,x) defined by p(0,x)=1, p(1,x)=-1-x, p(n,x)=((-1)^(n-1)-x)*p(n-1,x)-p(n-2,x) for n>=2 (0<=k<=n).
A124137 0 LD A signed aerated and skewed version of A038137.
A124377 0 FC Riordan array (1/(1-x-x^2),x/(1+x)).
A125100 0 LD Triangle read by rows: T(n,k)=fibonacci(k+1)*binom(n,k)+(k+1)*binom(n,k+1) (0<=k<=n).
A126198 0 SC Triangle read by rows: T(n,k) (1 <= k <= n) = number of compositions of n into parts of size <= k.
A126714 0 FC Dual Wythoff array read along antidiagonals.
A127647 0 LD Triangle read by rows: row n consists of n-1 zeros followed by Fibonacci(n).
A127711 0 LD Inverse of the triangle A(n,k)=if(k<=n,if(n<=2k,1/F(n+1),0),0).
A127711 0 SD Inverse of the triangle A(n,k)=if(k<=n,if(n<=2k,1/F(n+1),0),0).
A128097 0 LD Triangle read by rows: T(n,k) is the number of Motzkin paths of length n and having k steps that touch the x-axis (1<=k<=n).
A128206 0 SD Inverse of number triangle A128207.
A128540 0 LD A127647 * A097806.
A128540 0 SD A127647 * A097806.
A128541 0 LD A097806 * A127647.
A128541 0 SD A097806 * A127647.
A128544 0 LD A007318 * A128540.
A128585 0 LD A007318^(-1) * A128541.
A128589 0 LD A051731 * A127647.
A128619 0 LD A127647 * A128174.
A129713 0 FC Triangle read by rows: T(n,k) is the number of Fibonacci binary words of length n and starting with exactly k 1's (0<=k<=n). A Fibonacci binary word is a binary word having no 00 subword.
A129713 0 SC Triangle read by rows: T(n,k) is the number of Fibonacci binary words of length n and starting with exactly k 1's (0<=k<=n). A Fibonacci binary word is a binary word having no 00 subword.
A131331 0 FC A046854 * A000012(signed).
A131332 0 FC A065941 * A000012(signed).
A131333 0 FC A131332 * A000012.
A131333 0 SC A131332 * A000012.
A131336 0 FC A131334 * A000012.
A131344 0 FC A046854 * A065941.
A131345 0 FC A065941 * A046854.
A131410 0 FC A127647 * A000012.
A131410 0 LD A127647 * A000012.
A131410 0 SC A127647 * A000012.
A131410 0 SD A127647 * A000012.
A131411 0 FC A131410 + A104763 - A000012.
A131411 0 SC A131410 + A104763 - A000012.
A131606 0 SD Triangle read by rows: row n gives coefficients of the polynomial p(x, n) = Sum[Fibonacci[n]^i*x^(n - i), {i, 0, n}].
A131609 0 SC Mirror image of triangle in A131606.
A132919 0 FC (A127647 * A000012 + A000012 * A127648) - A000012.
A132923 0 LD Triangle by columns, F(n) followed by (F(n)+1), (F(n)+2), (F(n)+3),...
A134561 0 FC Array T by antidiagonals: T(n,k) = k-th number whose Zeckendorf representation has exactly n terms.
A135597 0 LD Square array read by antidiagonals: row m (m >= 1) satisfies b(0) = b(1) = 1; b(n) = m*b(n-1) + b(n-2):
A135966 0 SC Triangle, read by rows, where T(n,k) = fibonacci(k(n-k) + 1) for n>=k>=0.
A135966 0 SD Triangle, read by rows, where T(n,k) = fibonacci(k(n-k) + 1) for n>=k>=0.
A136170 1 SD Triangle T, read by rows, where row n of T = row n-1 of T^fibonacci(n) with appended '1' for n>=1 starting with a single '1' in row 0.
A136431 0 LD Hyperfibonacci number array read by antidiagonals.
A136531 0 FC Coefficients of polynomial recursion with simple values: a=-b;b=1;c=1 ; B(x, n) = ((1 + a + b)*x - c)*B(x, n - 1) - a*b*B(x, n - 2).
A137712 0 FC Triangle read by rows: T(n,k) = T(n-1, k-1) - T(n-k, k-1); with left border = the Fibonacci sequence.
A137712 0 SC Triangle read by rows: T(n,k) = T(n-1, k-1) - T(n-k, k-1); with left border = the Fibonacci sequence.
A137773 0 LD Triangular sequence: The Fibonacci sequence on the diagonal, 1's at all other places
A138201 0 FC A triangular sequence made up of the n-th Bonacci sequence b(n,m)=b_m[n]: the Kappraff triangle.
A139375 0 FC A Fibonacci-Catalan triangle. Also called the Fibonacci triangle.
A139821 0 FC Triangle T(i,j) read by rows: T(i,1) = Fibonacci(i) for all i; T(i,i) = i for all i; T(i,j) = T(i-1,j) + T(i-2,j) + T(i-1,j-1) - T(i-2,j-1).
A140835 0 FC A triangular sequence from a vector a(n) times a triangular tensor t(n,m): T(n,m)=a(n).t(n,m); a(n)=Fibonacci(n);A000045(n): t(n,m)=Binomial(n,GCD(n,m)).
A140835 0 LD A triangular sequence from a vector a(n) times a triangular tensor t(n,m): T(n,m)=a(n).t(n,m); a(n)=Fibonacci(n);A000045(n): t(n,m)=Binomial(n,GCD(n,m)).
A141169 0 LD Triangle of Fibonacci numbers, read by rows: T(n,k) = A000045(k), 0<=k<=n.
A141169 0 SD Triangle of Fibonacci numbers, read by rows: T(n,k) = A000045(k), 0<=k<=n.
A141539 0 SD Square array A(n,k) of numbers of length n binary words with at least k "0" between any two "1" digits (n,k >= 0), read by antidiagonals.
A143211 0 FC Triangle read by rows, T(n,k) = F(n)*F(k); 1<=k<=n.
A143211 0 SC Triangle read by rows, T(n,k) = F(n)*F(k); 1<=k<=n.
A144148 0 FC Weight array W={w(i,j)} of the Wythoff array A035513.
A144148 0 SC Weight array W={w(i,j)} of the Wythoff array A035513.
A144154 0 FC A Fibonacci triangle, row sums = A023610
A144154 0 SC A Fibonacci triangle, row sums = A023610
A144265 0 LD Triangle read by rows: prime numbers along left edge (n, 0) and Fibonacci numbers along right edge (n, n), with (n, k) = (n - 1, k - 1) + (n - 1, k) for 0 < k < n when n > 1.
A144287 0 LD Square array A(n,k), n>=1, k>=1, read by antidiagonals: A(n,k) = Fibonacci rabbit sequence number n coded in base k.
A144406 0 SD Rectangular array A read by upward antidiagonals: entry A(n,k) in row n and column k gives the number of compositions of k in which no part exceeds n, n>=1, k>=0.
A144409 0 SD Anti-diagonal expansion of: f(t,n)=If[n == 1, 1/(1 - t), 1/(1 - t^Floor[n/2] - t^n)].
A144428 0 LD Table read by antidiagonals: F(n) is a table of sequences representing the number of valid nodes in level n of a labeled binary tree, when the labeling rule forbids 1 of the 2^L states given by the last L digits of the parent label.
A152203 0 LD Triangle T(n,k) = (2n+1-2k)*fibonacci(k), read by rows.
A152440 0 FC Riordan matrix (1/(1-x-x^2),x/(1-x-x^2)^2).
A152462 0 FC A posterior vector Markov of A000045 as a triangular sequence: A back-iterated Markov with M=Inverse[{{0, 1}, {1, 1}}]={{-1, 1}, {1, 0}}; and v(0)={Fibonacci[n],Fibonacci[n-1]}, to give t(n,m)=v(m)=(M^m*v(0))_first_element. (Starting vector symmetrical in n,m.)
A152462 0 SC A posterior vector Markov of A000045 as a triangular sequence: A back-iterated Markov with M=Inverse[{{0, 1}, {1, 1}}]={{-1, 1}, {1, 0}}; and v(0)={Fibonacci[n],Fibonacci[n-1]}, to give t(n,m)=v(m)=(M^m*v(0))_first_element. (Starting vector symmetrical in n,m.)
A153281 0 LD Triangle read by rows, A130321 * A127647. Also, number of subsets of [n+2] with consecutive integers that start at k.
A153341 0 FC Triangle read by rows, A065941 * A007318
A154929 0 FC A Fibonacci convolution triangle.
A155002 0 FC Triangle read by rows, A104762 * (A000129 * 0^(n-k))
A155002 0 SC Triangle read by rows, A104762 * (A000129 * 0^(n-k))
A155112 0 SC Triangle T(n,k), 0<=k<=n, read by rows given by [0,2,-1/2,-1/2,0,0,0,0,0,0,0,0,...] DELTA [1,0,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938 .
A155161 0 SC Triangle T(n,k), 0<=k<=n, read by rows given by [0,1,1,-1,0,0,0,0,0,0,0,...] DELTA [1,0,0,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938 .
A156070 0 SC Triangle read by rows based on the Fibonacci sequence A000045: t(n,m) = 1 + Fibonacci[n] - Fibonacci[m] - Fibonacci[n - m].
A156070 0 SD Triangle read by rows based on the Fibonacci sequence A000045: t(n,m) = 1 + Fibonacci[n] - Fibonacci[m] - Fibonacci[n - m].
A157103 0 SC Triangle by columns, generalized Fibonacci sequences.
A159864 0 FC Difference array of Fibonacci numbers A000045 read by antidiagonals.
A159864 0 LD Difference array of Fibonacci numbers A000045 read by antidiagonals.
A159864 0 SC Difference array of Fibonacci numbers A000045 read by antidiagonals.
A159864 0 SD Difference array of Fibonacci numbers A000045 read by antidiagonals.
A160271 0 LD Monotonic justified array of all positive Fibonacci sequences.
A162303 0 FC Product matrix [C(k,n-k)]*A001263.
A164975 0 FC Triangle T(n,k) read by rows: T(n,k) = T(n-1,k)+2*T(n-1,k-1)+T(n-2,k)-T(n-2,k-1), T(n,0) = A000045(n),0<=k<=n-1.
A165357 0 FC Left-justified Wythoff Array.
A166291 0 FC Triangle read by rows: T(n,k) is the number of Dyck paths with no UUU's and no DDD's, of semilength n and having k peaks at odd level (0<=k<=n; U=(1,1), D=(1,-1)).
A166301 0 LD Triangle read by rows: T(n,k) is the number of Dyck paths of semilength n, having no ascents and no descents of length 1, and having pyramid weight k.
A169613 0 LD Triangular array: T(n,k)=floor(F(n),F(n-k)), k=1,2,...,n-2; n>=3, where F=A000045 (Fibonacci numbers).
A169614 0 LD Triangular array: T(n,k)=integer nearest F(n)/F(n-k), k=1,2,...,n-2; n>=3, where F=A000045 (Fibonacci numbers).
A169615 0 FC Triangular array: T(n,k)=floor(F(n+k)/F(k)), k=1,2,...,n-2; n>=3, where F=A000045 (Fibonacci numbers).
A169616 0 FC Triangular array: T(n,k)=integer nearest F(n+k)/F(k), k=1,2,...,n-2; n>=3, where F=A000045 (Fibonacci numbers).
A171729 0 FC Triangle of differences of Fibonacci numbers.
A171729 0 LD Triangle of differences of Fibonacci numbers.
A171729 0 SC Triangle of differences of Fibonacci numbers.
A171730 0 FC Triangle of differences of Fibonacci numbers.
A171730 0 LD Triangle of differences of Fibonacci numbers.
A171730 0 SD Triangle of differences of Fibonacci numbers.
A171731 0 FC Triangle T : T(n,k)= binomial(n,k)*Fibonacci(n-k)= A007318(n,k)*A000045(n-k).
A172236 0 LD Array t(n,k)=n*t(n,k-1)+t(n,k-2) read by antidiagonals, starting t(n,0)=0, t(n,1)=1.
A172237 0 LD Array t(n,k) = t(n-1,k)+k*t(n-2,k) read along falling antidiagonals, k>=1, n>=3. t(0,k) =0 and t(1,k)= t(2,k) =1 fixed.
A172371 0 SD Cubic recursion anti-diagonal triangle sequence: f(n,a)=a*f(n-2,a)+f(n-3,a)
A174430 0 FC Triangle read by rows: t(n,m)=GCD[Fibonacci[n],Fibonacci[m]]
A174430 0 LD Triangle read by rows: t(n,m)=GCD[Fibonacci[n],Fibonacci[m]]
A174802 0 SC Triangular sequence from anti-diagonal expansion of:p(x,m)=x*(x + 1)^(m - 1)/(1 - Sum[x^i, {i, 1, m}])
A175331 0 SC Array A092921(n,k) without the first two rows, read by antidiagonals.
A177350 0 LD Triangle read by rows: T(n,k)=Sum(binomial(n - (m + k), m + k), (m, 1, floor[n/2 + 1]))
A177351 0 LD Triangle t(n,k)= sum_{m=1..floor(n/2-k)} binomial(n-m-k,m+k), -floor(n/2) <= k <= floor(n/2), read by rows.
A177352 0 FC The triangle t(n,k) of the binomial sum as in A177351 in the column index range -floor(n/2)-1 <=k <= floor(n/2)-1.
A177352 0 LD The triangle t(n,k) of the binomial sum as in A177351 in the column index range -floor(n/2)-1 <=k <= floor(n/2)-1.
A178526 0 LD Triangle read by rows: T(n,k) is the number of nodes of cost k in the Fibonacci tree of order n.
A178526 0 SD Triangle read by rows: T(n,k) is the number of nodes of cost k in the Fibonacci tree of order n.
A178534 0 FC Triangle T(n,k) read by rows. T(n,1)=A000045(n+1), k>1: T(n,k) = (sum from i = 1 to k-1 of T(n-i,k-1)) - (sum from i = 1 to k-1 of T(n-i,k)).
A178534 0 SC Triangle T(n,k) read by rows. T(n,1)=A000045(n+1), k>1: T(n,k) = (sum from i = 1 to k-1 of T(n-i,k-1)) - (sum from i = 1 to k-1 of T(n-i,k)).
A179647 0 LD Rectangular array read by antidiagonals: T(n,k) is the number of compositions (ordered partitions) of n in which no part (summand) is equal to k.
A180165 0 LD Triangle read by rows, derived from an array of sequences generated from (1 + x)/ (1 - r*x - r*x^2)
A180760 0 SC T(n,k)=half the number of nXk binary arrays with each element equal to at least two neighbors
A180760 0 SD T(n,k)=half the number of nXk binary arrays with each element equal to at least two neighbors
A180771 0 FC T(n,k)=half the number of nXk binary arrays with each element equal to at least one neighbor
A180771 0 LD T(n,k)=half the number of nXk binary arrays with each element equal to at least one neighbor
A180835 1 SD T(n,k)=number of n-bit binary numbers with every initial substring not divisible by k
A181031 0 SC Array read by antidiagonals: T(n,k) = number of nXk binary matrices with no initial bit string in any row or column divisible by 4
A181031 0 SD Array read by antidiagonals: T(n,k) = number of nXk binary matrices with no initial bit string in any row or column divisible by 4
A181206 0 FC T(n,k) = number of n X k matrices containing a permutation of 1..n*k moving each element at most to a neighboring position.
A181206 0 LD T(n,k) = number of n X k matrices containing a permutation of 1..n*k moving each element at most to a neighboring position.
A181974 0 FC Triangle T(n,k), read by rows, given by (1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, -3, 2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
A183312 0 FC T(n,k)=Half the number of nXk binary arrays with no element equal to a strict majority of its horizontal and vertical neighbors
A183312 0 LD T(n,k)=Half the number of nXk binary arrays with no element equal to a strict majority of its horizontal and vertical neighbors
A183322 0 FC T(n,k)=Number of nXk binary arrays with an element zero only if there are an even number of ones to its left and an even number of ones above it
A183322 0 LD T(n,k)=Number of nXk binary arrays with an element zero only if there are an even number of ones to its left and an even number of ones above it
A183335 0 FC T(n,k)=Number of nXk binary arrays with each 1 adjacent to exactly two 0s
A183335 0 LD T(n,k)=Number of nXk binary arrays with each 1 adjacent to exactly two 0s
A183386 0 FC T(n,k)=Half the number of nXk binary arrays with no element equal to a strict majority of its king-move neighbors
A183386 0 LD T(n,k)=Half the number of nXk binary arrays with no element equal to a strict majority of its king-move neighbors
A183391 0 FC T(n,k)=Half the number of nXk binary arrays with no element unequal to a strict majority of its king-move neighbors
A183391 0 LD T(n,k)=Half the number of nXk binary arrays with no element unequal to a strict majority of its king-move neighbors
A183391 0 SC T(n,k)=Half the number of nXk binary arrays with no element unequal to a strict majority of its king-move neighbors
A183391 0 SD T(n,k)=Half the number of nXk binary arrays with no element unequal to a strict majority of its king-move neighbors
A185081 0 LD Triangle T(n,k), read by rows, given by (0, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
A185081 0 SC Triangle T(n,k), read by rows, given by (0, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
A185384 0 LD A binomial transform of Fibonacci numbers.
A185675 0 FC Riordan array ( (1+x)/(1-x-x^2), x*A000108(x) ).
A185736 0 FC Weight array of the Wythoff array, by antidiagonals.
A185736 0 SC Weight array of the Wythoff array, by antidiagonals.
A185813 0 FC Riordan array (A000045(x),x*A005043(x)).
A185835 0 FC T(n,k)=Half the number of nXk binary arrays with every element equal to exactly one or two of its horizontal and vertical neighbors
A185835 0 LD T(n,k)=Half the number of nXk binary arrays with every element equal to exactly one or two of its horizontal and vertical neighbors
A185937 0 FC Riordan array (A000045(x)^m, x*A000108(x)), m=1.
A187596 1 SD Array T(m,n) read by antidiagonals: number of domino tilings of the m X n grid (m>=0, n>=0).
A188706 0 LD T(n,k)=Number of nXk binary arrays without the pattern 0 0 diagonally or vertically
A189006 1 SD Array A(m,n) read by antidiagonals: number of domino tilings of the m X n grid with upper left corner removed iff m*n is odd, (m>=0, n>=0).
A189254 0 FC T(n,k)=Number of nXk array permutations with each element making zero or one king moves
A189254 0 LD T(n,k)=Number of nXk array permutations with each element making zero or one king moves
A189312 0 FC T(n,k)=Number of nXk array permutations with each element moving zero or one space diagonally, horizontally or vertically
A189312 0 LD T(n,k)=Number of nXk array permutations with each element moving zero or one space diagonally, horizontally or vertically
A189435 0 SC T(n,k)=Number of nXk array permutations with each element not moving, or moving one space N, SW or SE
A189449 0 FC T(n,k)=Number of nXk array permutations with each element moving zero or one space horizontally or diagonally
A189650 0 FC T(n,k)=Number of nXk array permutations with each element moving zero or one space horizontally, diagonally or antidiagonally
A189675 0 LD Composition of Catalan and Fibonacci numbers.
A192062 0 SD Square Array T(ij) read by anti-diagonals (from NE to SW) with columns 2j being the denominators of continued fraction convergents to square root of (j^2 + 2j).
A193376 0 LD T(n,k) = number of ways to place any number of 2 X 1 tiles of k distinguishable colors into an n X 1 grid.
A193588 0 LD A Fibonacci triangle: p(n,k)=F(k+2) for 0<=k<=n.
A193588 0 SD A Fibonacci triangle: p(n,k)=F(k+2) for 0<=k<=n.
A193736 0 LD Triangular array: the fusion of polynomial sequences P and Q given by p(n,x)=(n+1)st Fibonacci polynomial and q(n,x)=(x+1)^n.
A193737 0 FC Mirror of the triangle A193736.
A193906 0 FC Triangular array: the self-fusion of (p(n,x)), where p(n,x)=sum{F(k+2)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers).
A193907 0 LD Mirror of the triangle A193906.
A193917 0 FC Triangular array: the self-fusion of (p(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers).
A193917 0 SC Triangular array: the self-fusion of (p(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers).
A193918 0 LD Mirror of the triangle A193917.
A193918 0 SD Mirror of the triangle A193917.
A193919 0 FC Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers), and q(n,x)=(x+1)^n.
A193920 0 LD Mirror of the triangle A193919.
A193921 0 FC Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers), and q(n,x)=x^n+x^(n-1)+...+x+1.
A193921 0 SC Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers), and q(n,x)=x^n+x^(n-1)+...+x+1.
A193922 0 LD Mirror of the triangle A193921.
A193922 0 SD Mirror of the triangle A193921.
A193953 0 FC Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers), and q(n,x)=x*q[n-1,x}+n+1, n>=0.
A193953 0 SC Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers), and q(n,x)=x*q[n-1,x}+n+1, n>=0.
A193954 0 LD Mirror of the triangle A193953.
A193954 0 SD Mirror of the triangle A193953.
A193955 0 FC Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers), and q(n,x)=sum{((k+1)^2)*x^(n-k) : 0<=k<=n}.
A193956 0 LD Mirror of the triangle A193955.
A193969 0 FC Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers) and q(n,x)=sum{L(k+1)*x^(n-k) : 0<=k<=n}, where F=A000032 (Lucas numbers).
A193970 0 LD Mirror of the triangle A193969.
A193997 0 FC Triangular array: the fission of (p(n,x)) by (q(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers) and q(n,x)=(x+1^n.
A193998 0 LD Mirror of the triangle A193997.
A193999 0 LD Mirror of the triangle A094585.
A193999 0 SD Mirror of the triangle A094585.
A194000 0 FC Triangular array: the self-fission of (p(n,x)), where sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers).
A194000 0 SC Triangular array: the self-fission of (p(n,x)), where sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers).
A194001 0 LD Mirror of the triangle A194000.
A194001 0 SD Mirror of the triangle A194000.
A194007 0 FC Triangular array: the fission of (p(n,x)) by (q(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers) and q(n,x)=x*q(n-1,x)+n+1, with q(0,x)=1.
A194008 0 LD Mirror of the triangle A194007.
A194030 0 FC Natural interspersion of the Fibonacci sequence (1,2,3,5,8,...), a rectangular array, by antidiagonals.
A194056 0 SC Natural interspersion of A000071(Fibonacci numbers minus 1), a rectangular array, by antidiagonals.
A196322 0 FC T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 1,3,0,2,4 for x=0,1,2,3,4
A196322 0 LD T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 1,3,0,2,4 for x=0,1,2,3,4
A196329 0 FC T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 1,3,0,4,2 for x=0,1,2,3,4
A196329 0 LD T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 1,3,0,4,2 for x=0,1,2,3,4
A196343 0 FC T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 1,4,0,2,3 for x=0,1,2,3,4
A196343 0 LD T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 1,4,0,2,3 for x=0,1,2,3,4
A196590 0 FC T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,2,0,1,4 for x=0,1,2,3,4
A196590 0 LD T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,2,0,1,4 for x=0,1,2,3,4
A196653 0 FC T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,4,0,2,1 for x=0,1,2,3,4
A196653 0 LD T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,4,0,2,1 for x=0,1,2,3,4
A196802 0 FC T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,2,0,4,1 for x=0,1,2,3,4
A196802 0 LD T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,2,0,4,1 for x=0,1,2,3,4
A196929 1 SD T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 1,4,3,2,0 for x=0,1,2,3,4
A196974 0 FC T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,3,0,2,1 for x=0,1,2,3,4
A196974 0 LD T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,3,0,2,1 for x=0,1,2,3,4
A197047 0 FC T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,2,0,1,3 for x=0,1,2,3,4
A197047 0 LD T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,2,0,1,3 for x=0,1,2,3,4
A197098 0 FC T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,4,0,0,1 for x=0,1,2,3,4
A197098 0 LD T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,4,0,0,1 for x=0,1,2,3,4
A197235 0 FC T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,3,0,1,2 for x=0,1,2,3,4
A197235 0 LD T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,3,0,1,2 for x=0,1,2,3,4
A197307 0 FC T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,4,0,2,1 for x=0,1,2,3,4
A197307 0 LD T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,4,0,2,1 for x=0,1,2,3,4
A197457 0 FC T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,3,0,2,2 for x=0,1,2,3,4
A197457 0 LD T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,3,0,2,2 for x=0,1,2,3,4
A197561 0 FC T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,3,0,2,2 for x=0,1,2,3,4
A197561 0 LD T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,3,0,2,2 for x=0,1,2,3,4
A197750 0 FC T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,3,0,1,0 for x=0,1,2,3,4
A197750 0 LD T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,3,0,1,0 for x=0,1,2,3,4
A197896 0 FC T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,3,0,1,1 for x=0,1,2,3,4
A197896 0 LD T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,3,0,1,1 for x=0,1,2,3,4
A198013 0 FC T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,3,0,1,2 for x=0,1,2,3,4
A198013 0 LD T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,3,0,1,2 for x=0,1,2,3,4
A198155 0 FC T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,3,0,1,1 for x=0,1,2,3,4
A198155 0 LD T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,3,0,1,1 for x=0,1,2,3,4
A199334 0 FC Triangle T(n,k) = Fibonacci(n+k), related to A000045 (Fibonacci numbers).
A199334 0 SC Triangle T(n,k) = Fibonacci(n+k), related to A000045 (Fibonacci numbers).
A199512 0 FC Triangle T(n,k) = Fibonacci(n+k+1), related to A000045 (Fibonacci numbers).
A199512 0 SC Triangle T(n,k) = Fibonacci(n+k+1), related to A000045 (Fibonacci numbers).
A199535 0 FC Clark Kimberling's even first column Stolarsky array read by antidiagonals.
A200251 0 LD T(n,k)=Number of 0..k arrays x(0..n-1) of n elements with each no smaller than the sum of its previous elements modulo (k+1)
A201947 0 FC Triangle T(n,k), read by rows, given by (1,1,-1,0,0,0,0,0,0,0,...) DELTA (1,-1,1,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938.
A202389 0 LD Triangle T(n,k), read by rows, given by (1, -2, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
A202389 0 SD Triangle T(n,k), read by rows, given by (1, -2, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
A202390 0 LD Triangle T(n,k), read by rows, given by (1, 0, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
A202395 0 LD Triangle T(n,k), read by rows, given by (1, 1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
A202396 0 LD Triangle T(n,k), read by rows, given by (2, 1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (2, -1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
A202451 0 LD Upper triangular Fibonacci matrix, by SW antidiagonals.
A202451 0 SD Upper triangular Fibonacci matrix, by SW antidiagonals.
A202452 0 FC Lower triangular Fibonacci matrix, by SW antidiagonals.
A202452 0 SC Lower triangular Fibonacci matrix, by SW antidiagonals.
A202453 0 FC Fibonacci self-fusion matrix, by antidiagonals.
A202453 0 LD Fibonacci self-fusion matrix, by antidiagonals.
A202453 0 SC Fibonacci self-fusion matrix, by antidiagonals.
A202453 0 SD Fibonacci self-fusion matrix, by antidiagonals.
A202502 0 LD Modified lower triangular Fibonacci matrix, by antidiagonals.
A202502 0 SD Modified lower triangular Fibonacci matrix, by antidiagonals.
A202503 0 FC Fibonacci self-fission matrix, by antidiagonals.
A202503 0 LD Fibonacci self-fission matrix, by antidiagonals.
A202503 0 SC Fibonacci self-fission matrix, by antidiagonals.
A202503 0 SD Fibonacci self-fission matrix, by antidiagonals.
A202874 0 FC Symmetric matrix based on (1,2,3,5,8,13,...), by antidiagonals.
A202874 0 LD Symmetric matrix based on (1,2,3,5,8,13,...), by antidiagonals.
A203362 0 FC T(n,k)=Number of nXk binary arrays with every 1 immediately preceded by 0 to the left or above
A203362 0 LD T(n,k)=Number of nXk binary arrays with every 1 immediately preceded by 0 to the left or above
A203371 0 FC T(n,k)=Number of nXk 0..2 arrays with every 1 immediately preceded by 0 to the left or above, and every 2 immediately preceded by both a 1 and a 0
A203371 0 LD T(n,k)=Number of nXk 0..2 arrays with every 1 immediately preceded by 0 to the left or above, and every 2 immediately preceded by both a 1 and a 0
A204197 0 FC T(n,k)=Number of nXk 0..1 arrays with no occurence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..1 introduced in row major order
A204197 0 LD T(n,k)=Number of nXk 0..1 arrays with no occurence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..1 introduced in row major order
A204922 0 LD Ordered differences of Fibonacci numbers.
A204922 0 SD Ordered differences of Fibonacci numbers.
A205573 0 SD Array M read by antidiagonals in which successive rows evidently converge to A001405 (central binomial coefficients).
A205575 0 FC Triangle read by rows, related to Pascal's triangle.
A205575 0 LD Triangle read by rows, related to Pascal's triangle.
A207611 0 FC Triangle of coefficients of polynomials v(n,x) jointly generated with A207610; see Formula section.
A207613 0 FC Triangle of coefficients of polynomials v(n,x) jointly generated with A207612; see Formula section.
A207632 0 FC Triangle of coefficients of polynomials v(n,x) jointly generated with A207631; see Formula section.
A207634 0 FC Triangle of coefficients of polynomials v(n,x) jointly generated with A207633; see Formula section.
A208336 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A208337; see the Formula section.
A208337 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A208836; see the Formula section.
A208340 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A202390; see the Formula section.
A208342 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A208343; see the Formula section.
A208343 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A208342; see the Formula section.
A208459 0 LD Triangle T_x = T(n,k) given by (0, 1/x, 1-1/x, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (x, 1/x-1, -1/x, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938, for x = 0.
A208514 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A208515; see the Formula section.
A208515 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A208514; see the Formula section.
A208518 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A208519; see the Formula section.
A208519 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A208518; see the Formula section.
A208608 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A208609; see the Formula section.
A208609 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A208608; see the Formula section.
A208612 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A208613; see the Formula section.
A208613 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A208612; see the Formula section.
A209125 0 FC Triangle of coefficients of polynomials u(n,x) jointly generated with A164975; see the Formula section.
A209126 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A209127; see the Formula section.
A209127 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A209126; see the Formula section.
A209130 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A102756; see the Formula section.
A209137 0 FC Triangle of coefficients of polynomials u(n,x) jointly generated with A209138; see the Formula section.
A209137 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A209138; see the Formula section.
A209138 0 FC Triangle of coefficients of polynomials v(n,x) jointly generated with A209137; see the Formula section.
A209138 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A209137; see the Formula section.
A209139 0 FC Triangle of coefficients of polynomials u(n,x) jointly generated with A209140; see the Formula section.
A209140 0 FC Triangle of coefficients of polynomials v(n,x) jointly generated with A209139; see the Formula section.
A209141 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A209142; see the Formula section.
A209142 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A209141; see the Formula section.
A209147 0 FC Triangle of coefficients of polynomials v(n,x) jointly generated with A209146; see the Formula section.
A209151 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A208337; see the Formula section.
A209153 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A208340; see the Formula section.
A209166 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A209167; see the Formula section.
A209167 0 FC Triangle of coefficients of polynomials v(n,x) jointly generated with A209166; see the Formula section.
A209167 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A209166; see the Formula section.
A209169 0 FC Triangle of coefficients of polynomials v(n,x) jointly generated with A209168; see the Formula section.
A209170 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A209171; see the Formula section.
A209171 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A209170; see the Formula section.
A209419 0 FC Triangle of coefficients of polynomials u(n,x) jointly generated with A209420; see the Formula section.
A209420 0 FC Triangle of coefficients of polynomials v(n,x) jointly generated with A209419; see the Formula section.
A209434 0 FC Table T(n,m), read by antidiagonals, is the number of subsets of {1,...,n} which do not contain two elements whose difference is m+1.
A209435 0 LD Table T(m,n), read by antidiagonals, is the number of subsets of {1,...,n} which do not contain two elements whose difference is m+1.
A209599 0 FC Triangle T(n,k), read by rows, given by (2, -1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
A209703 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A209704; see the Formula section.
A209704 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A209703; see the Formula section.
A209745 0 FC Triangle of coefficients of polynomials u(n,x) jointly generated with A209746; see the Formula section.
A209746 0 FC Triangle of coefficients of polynomials v(n,x) jointly generated with A209745; see the Formula section.
A209755 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A209756; see the Formula section.
A209756 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A209755; see the Formula section.
A209769 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A209770; see the Formula section.
A209770 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A209769; see the Formula section.
A209972 2 SD Number of binary words of length n avoiding the subword given by the binary expansion of k; square array A(n,k), n>=0, k>=0, read by antidiagonals.
A210221 0 SC Triangle of coefficients of polynomials u(n,x) jointly generated with A210596; see the Formula section.
A210239 0 LD Triangle, read by rows, given by (2, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (2, -1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
A210341 0 SC Triangle generated by T(n,k) = Fibonacci(n-k+2)^k.
A210552 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A210553; see the Formula section.
A210553 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A210552; see the Formula section.
A210559 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A210560; see the Formula section.
A210560 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A210559; see the Formula section.
A210565 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A210595; see the Formula section.
A210595 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A209999; see the Formula section.
A210596 0 FC Triangle of coefficients of polynomials v(n,x) jointly generated with A210221; see the Formula section.
A210637 0 LD Triangle T(n,k), read by rows, given by (2, 1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (2, -1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
A210662 0 FC Triangle read by rows: T(n,k) (1 <= k <= n) = number of monomer-dimer tilings of an n X k board.
A210789 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A210790; see the Formula section.
A210790 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A210789; see the Formula section.
A210791 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A210792; see the Formula section.
A210792 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A210791; see the Formula section.
A210793 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A210794; see the Formula section.
A210794 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A210793; see the Formula section.
A210795 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A210796; see the Formula section.
A210796 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A210795; see the Formula section.
A210797 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A210798; see the Formula section.
A210798 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A210797; see the Formula section.
A210799 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A210800; see the Formula section.
A210800 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A210799; see the Formula section.
A210801 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A210802; see the Formula section.
A210802 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A210801; see the Formula section.
A210803 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A210804; see the Formula section.
A210804 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A210803; see the Formula section.
A210805 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A210806; see the Formula section.
A210806 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A210805; see the Formula section.
A210858 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A210859; see the Formula section.
A210859 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A210858; see the Formula section.
A210860 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A210861; see the Formula section of A210861.
A210861 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A210860; see the Formula section.
A210862 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A210863; see the Formula section.
A210863 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A210862; see the Formula section.
A210864 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A210865; see the Formula section.
A210865 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A210864; see the Formula section.
A210866 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A210867; see the Formula section.
A210867 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A210866; see the Formula section.
A210868 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A210869; see the Formula section.
A210868 0 SD Triangle of coefficients of polynomials u(n,x) jointly generated with A210869; see the Formula section.
A210869 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A210868; see the Formula section.
A210870 0 LD Triangle of coefficients of polynomials u(n,x) jointly generated with A210871; see the Formula section.
A210870 0 SD Triangle of coefficients of polynomials u(n,x) jointly generated with A210871; see the Formula section.
A210871 0 LD Triangle of coefficients of polynomials v(n,x) jointly generated with A210870; see the Formula section.
A210871 0 SD Triangle of coefficients of polynomials v(n,x) jointly generated with A210870; see the Formula section.
A210875 0 LD Triangular array U(n,k) of coefficients of polynomials defined in Comments.
A210880 0 LD Triangular array U(n,k) of coefficients of polynomials defined in Comments.
A212402 0 LD T(n,k)=Number of binary arrays of length n+2*k-1 with no more than k ones in any length 2k subsequence (=50% duty cycle)
A212729 0 LD T(n,k)=Number of 0..2 arrays of length n+2*k-1 with sum less than 2*k in any length 2k subsequence (=less than 50% duty cycle)
A212782 0 LD T(n,k)=Half the number of 0..k arrays of length n+2 with second differences nonzero
A213576 0 LD Rectangular array: (row n) = b**c, where b(h) = h, c(h) = F(n-1+h), where F=A000045 (Fibonacci numbers), n>=1, h>=1, and ** = convolution.
A213587 0 LD Rectangular array: (row n) = b**c, where b(h) = F(h+1), c(h) = F(n+h), F = A000045 (Fibonacci numbers), n>=1, h>=1, and ** = convolution.
A213590 0 LD Rectangular array: (row n) = b**c, where b(h) = h^2, c(h) = F(n-1+h), F = A000045 (Fibonacci numbers), n>=1, h>=1, and ** = convolution.
A213765 0 LD Rectangular array: (row n) = b**c, where b(h) = 2*n-1, c(h) = F(n-1+h), F=A000045 (Fibonacci numbers), n>=1, h>=1, and ** = convolution.
A213777 0 LD Rectangular array: (row n) = b**c, where b(h) = F(h), c(h) = F(h+1), F=A000045 (Fibonacci numbers), n>=1, h>=1, and ** = convolution.
A213777 0 SD Rectangular array: (row n) = b**c, where b(h) = F(h), c(h) = F(h+1), F=A000045 (Fibonacci numbers), n>=1, h>=1, and ** = convolution.
A214178 0 FC Triangle T(n,k) by rows: the k-th derivative of the Fibonacci Polynomial F_n(x) evaluated at x=1.
A214582 0 FC Riordan array (1/(1-x-x^2), x*(1+2*x)).
A214978 0 FC Array T[(m,n) = F(m*n)/F(m), where F = A000045 (Fibonacci numbers), by antidiagonals; transpose of A028412.
A214987 0 SC Power round array for the golden ratio, by antidiagonals.
A217762 0 LD Square array T, read by antidiagonals: T(n,k) = F(n) + 2*F(k) where F(n) is the n-th Fibonacci number.
A219924 1 SD Number A(n,k) of tilings of a k X n rectangle using integer sided square tiles; square array A(n,k), n>=0, k>=0, read by antidiagonals.
A220122 1 SD Number A(n,k) of tilings of a k X n rectangle using integer sided rectangular tiles of area k; square array A(n,k), n>=0, k>=0, read by antidiagonals.
A220553 0 FC T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor
A220553 0 LD T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor
A220562 0 FC T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly one horizontal or antidiagonal neighbor
A220614 0 SC T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two horizontal and vertical neighbors, without consecutive collinear links
A220614 0 SD T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two horizontal and vertical neighbors, without consecutive collinear links
A220621 0 FC T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly one horizontal, diagonal and antidiagonal neighbor
A220632 1 SD T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two horizontal or antidiagonal neighbors
A220644 0 FC T(n,k) = number of ways to reciprocally link elements of an n X k array either to themselves or to exactly one king-move neighbor.
A220644 0 LD T(n,k) = number of ways to reciprocally link elements of an n X k array either to themselves or to exactly one king-move neighbor.
A220708 0 SC T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links
A221459 0 LD T(n,k)=Number of 0..k arrays of length n with each element unequal to at least one neighbor, with new values introduced in 0..k order
A221463 0 LD T(n,k)=Number of 0..k arrays of length n with each element unequal to at least one neighbor, starting with 0
A221515 0 SD T(n,k)=Number of 0..k arrays of length n with each element differing from at least one neighbor by 2 or more, starting with 0
A221542 0 LD T(n,k)=Number of 0..k arrays of length n with each element differing from at least one neighbor by something other than 1, starting with 0
A226444 1 SD Number A(n,k) of tilings of a k X n rectangle using 1 X 1 squares and L-tiles; square array A(n,k), n>=0, k>=0, read by antidiagonals.
A227431 0 FC Fibonacci differences triangle, T(n,k), k<=n, where column k holds the k-th difference of A000045, read by rows.
A227431 0 LD Fibonacci differences triangle, T(n,k), k<=n, where column k holds the k-th difference of A000045, read by rows.
A227431 0 SC Fibonacci differences triangle, T(n,k), k<=n, where column k holds the k-th difference of A000045, read by rows.
A228074 0 FC A Fibonacci-Pascal triangle read by rows: T(n,0) = Fibonacci(n), T(n,n) = n and for n > 0: T(n,k) = T(n-1,k-1) + T(n-1,k), 0 < k < n.
A228074 0 SC A Fibonacci-Pascal triangle read by rows: T(n,0) = Fibonacci(n), T(n,n) = n and for n > 0: T(n,k) = T(n-1,k-1) + T(n-1,k), 0 < k < n.
A228285 0 FC T(n,k) = Number of n X k binary arrays with top left value 1 and no two ones adjacent horizontally, vertically or nw-se diagonally.
A228285 0 LD T(n,k) = Number of n X k binary arrays with top left value 1 and no two ones adjacent horizontally, vertically or nw-se diagonally.
A228390 0 FC T(n,k)=Number of nXk binary arrays with top left value 1 and no two ones adjacent horizontally or vertically.
A228390 0 LD T(n,k)=Number of nXk binary arrays with top left value 1 and no two ones adjacent horizontally or vertically.
A228482 0 FC T(n,k)=Number of nXk binary arrays with top left value 1 and no two ones adjacent horizontally, vertically or antidiagonally.
A228482 0 LD T(n,k)=Number of nXk binary arrays with top left value 1 and no two ones adjacent horizontally, vertically or antidiagonally.
A228506 0 FC T(n,k)=Number of nXk binary arrays with top left value 1 and no two ones adjacent horizontally, vertically, diagonally or antidiagonally.
A228506 0 LD T(n,k)=Number of nXk binary arrays with top left value 1 and no two ones adjacent horizontally, vertically, diagonally or antidiagonally.
A228660 0 FC T(n,k)=Number of nXk binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.
A228683 0 FC T(n,k)=Number of nXk binary arrays with no two ones adjacent horizontally, diagonally or antidiagonally.
A228754 0 FC T(n,k)=Number of nXk binary arrays with top left element equal to 1 and no two ones adjacent horizontally or antidiagonally.
A228796 0 FC T(n,k)=Number of nXk binary arrays with top left element equal to 1 and no two ones adjacent horizontally or nw-se.
A228815 0 FC Symmetric triangle, read by rows, related to Fibonacci numbers.
A228815 0 LD Symmetric triangle, read by rows, related to Fibonacci numbers.
A229556 0 SD Array read by antidiagonals. Rows are the numerators of consecutive harmonic transforms starting with a first row 1, 1, 1,....
A229557 0 SD Array read by antidiagonals. Rows are the denominators of consecutive harmonic transforms starting with a first row 1, 1, 1,....
A230989 0 FC T(n,k)=Number of white square subarrays of (n+1)X(k+1) binary arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with upper left element zero
A230989 0 LD T(n,k)=Number of white square subarrays of (n+1)X(k+1) binary arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with upper left element zero
A231070 0 FC T(n,k)=Number of black square subarrays of (n+1)X(k+1) binary arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with upper left element zero
A231070 0 LD T(n,k)=Number of black square subarrays of (n+1)X(k+1) binary arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with upper left element zero
A231154 0 LD Triangular array read by rows: row n shows the coefficients of the polynomial u(n) = c(0) + c(1)*x + ... + c(n)*x^n which is the numerator of the n-th convergent of the continued fraction [k, k, k, ... ], where k = (x + 1)/(x - 1).
A231154 0 SD Triangular array read by rows: row n shows the coefficients of the polynomial u(n) = c(0) + c(1)*x + ... + c(n)*x^n which is the numerator of the n-th convergent of the continued fraction [k, k, k, ... ], where k = (x + 1)/(x - 1).
A231727 0 LD Triangular array read by rows: row n shows the coefficients of the polynomial u(n) = c(0) + c(1)*x + ... + c(n)*x^n which is the denominator of the n-th convergent of the continued fraction [k, k, k, ... ], where k = (x + 1)/(x - 1).
A231727 0 SD Triangular array read by rows: row n shows the coefficients of the polynomial u(n) = c(0) + c(1)*x + ... + c(n)*x^n which is the denominator of the n-th convergent of the continued fraction [k, k, k, ... ], where k = (x + 1)/(x - 1).
A231731 0 LD Triangular array read by rows: row n shows the coefficients of the polynomial u(n) = c(0) + c(1)*x + ... + c(n)*x^(n) which is the numerator of the n-th convergent of the continued fraction [k, k, k, ... ], where k = 2*x + 1.
A231732 0 SD Triangular array read by rows: row n shows the coefficients of the polynomial u(n) = c(0) + c(1)*x + ... + c(n)*x^(n) which is the numerator of the n-th convergent of the continued fraction [k, k, k, ... ], where k = (x + 2)/(x + 1).
A231733 0 SD Triangular array read by rows: row n shows the coefficients of the polynomial u(n) = c(0) + c(1)*x + ... + c(n)*x^(n) which is the denominator of the n-th convergent of the continued fraction [k, k, k, ... ], where k = (x + 2)/(x + 1).
A231774 0 SD Triangular array read by rows: row n shows the coefficients of the polynomial u(n) = c(0) + c(1)*x + ... + c(n)*x^(n) which is the numerator of the n-th convergent of the continued fraction [k, k, k, ... ], where k = (x + 1)/(x + 2).
A231775 0 SD Triangular array read by rows: row n shows the coefficients of the polynomial u(n) = c(0) + c(1)*x + ... + c(n)*x^(n) which is the denominator of the n-th convergent of the continued fraction [k, k, k, ... ], where k = (x + 1)/(x + 2).
A234357 0 LD Array T(n,k) by antidiagonals: T(n,k) = n^k * Fibonacci(k).
A234713 0 FC Triangle, read by rows, based on the Fibonacci numbers.
A236076 0 LD A skewed version of triangular array A122075.
A237498 0 FC Riordan array (1/(1-x-x^2), x/(1+2*x)).
A238654 0 FC T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with no element equal to all horizontal neighbors or equal to all vertical neighbors, and new values 0..1 introduced in row major order
A238654 0 LD T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with no element equal to all horizontal neighbors or equal to all vertical neighbors, and new values 0..1 introduced in row major order
A238888 0 SD Number A(n,k) of self-inverse permutations p on [n] with displacement of elements restricted by k: |p(i)-i| <= k, square array A(n,k), n>=0, k>=0, read by antidiagonals.
A240519 0 FC T(n,k)=Number of nXk 0..1 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..1 introduced in row major order
A240519 0 LD T(n,k)=Number of nXk 0..1 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..1 introduced in row major order
A240649 0 FC T(n,k)=Number of nXk 0..1 arrays with no element equal to the same number of vertical neighbors as horizontal neighbors, with new values 0..1 introduced in row major order
A240649 0 LD T(n,k)=Number of nXk 0..1 arrays with no element equal to the same number of vertical neighbors as horizontal neighbors, with new values 0..1 introduced in row major order
A242086 0 SC Triangle read by rows: T(n,k) is the number of compositions of n into odd parts with first part k.
A242239 0 LD T(n,k)=Number of length n+k+1 0..k arrays with every value 0..k appearing at least once in every consecutive k+2 elements, and new values 0..k introduced in order
A242472 0 LD T(n,k)=Number of length n+2 0..k arrays with no three equal elements in a row and new values 0..k introduced in 0..k order
A243607 0 LD T(n,k)=Number of length n+2 0..k arrays with no three elements in a row with pattern aba (with a!=b) and new values 0..k introduced in 0..k order
A243729 0 LD T(n,k)=Number of length n+2 0..k arrays with no three unequal elements in a row and no three equal elements in a row and new values 0..k introduced in 0..k order
A245013 1 SD Number A(n,k) of tilings of a k X n rectangle using 1 X 1 squares and 2 X 2 squares; square array A(n,k), n>=0, k>=0, read by antidiagonals.
A245049 0 LD Number A(n,k) of hybrid k-ary trees with n internal nodes; square array A(n,k), n>=0, k>=1, read by antidiagonals.
A246690 2 SD Number A(n,k) of compositions of n into parts of the k-th list of distinct parts in the order given by A246688; square array A(n,k), n>=0, k>=0, read by antidiagonals.
A247489 0 SD Square array read by antidiagonals: A(k, n) = hypergeometric(P, Q, -k^k/(k-1)^(k-1)) rounded to the nearest integer, P = [(j-n)/k, j=0..k-1] and Q = [(j-n)/(k-1), j=0..k-2], k>=1, n>=0.
A247506 1 SD Generalized Fibonacci numbers: square array A(n,k) read by antidiagonals, A(n,k) = [x^k]((1-sum_{j=1..n} x^j)^(-1)), (n>=0, k>=0).
A256658 0 LD Rectangular array by antidiagonals: row n consists of numbers k such that F(n+1) is the trace of the minimal alternating Fibonacci representation of k, where F = A000045 (Fibonacci numbers).
A256661 0 FC Rectangular array by antidiagonals: row n shows the numbers k such that R(k) consists of n terms, where R(k) is the minimal alternating Fibonacci representation of k.
A259708 0 LD Triangle T(n,k) (0 <= k <= n) giving coefficients of certain polynomials related to Fibonacci numbers.
A263597 0 LD T(n,k)=Number of length n arrays of permutations of 0..n-1 with each element moved by -k to k places and the median of every three consecutive elements nondecreasing.
A263683 0 LD T(n,k)=Number of length n arrays of permutations of 0..n-1 with each element moved by -k to k places and with no two consecutive decreases.
A263703 0 LD T(n,k)=Number of length n arrays of permutations of 0..n-1 with each element moved by -k to k places and every three consecutive elements having its maximum within 4 of its minimum.
A263744 0 LD T(n,k)=Number of length n arrays of permutations of 0..n-1 with each element moved by -k to k places and equal numbers of elements moved upwards and downwards
A263752 0 LD T(n,k)=Number of length n arrays of permutations of 0..n-1 with each element moved by -k to k places and every three consecutive elements having its maximum within 5 of its minimum
A263905 0 LD T(n,k)=Number of length n arrays of permutations of 0..n-1 with each element moved by -k to k places and the total absolute value of displacements not greater than 2*(n-1).
A263939 0 LD T(n,k)=Number of length n arrays of permutations of 0..n-1 with each element moved by -k to k places and the total absolute value of displacements not greater than n.
A264244 0 LD T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having directed index change 0,0 1,1 0,-1 -1,1 or 0,-2.
A269750 0 LD Triangle read by rows: row n gives coefficients of Schur polynomial Omega(n) in order of decreasing powers of x.
A271315 0 FC Array T(n,k) read by diagonals: T(n,k) = T(n,k-1) + T(n,k-2) where T(n,0) = F(n+1), T(n,1) = F(n); F(n) = Fibonacci(n) = A000045(n).
A271315 0 LD Array T(n,k) read by diagonals: T(n,k) = T(n,k-1) + T(n,k-2) where T(n,0) = F(n+1), T(n,1) = F(n); F(n) = Fibonacci(n) = A000045(n).
A271315 0 SC Array T(n,k) read by diagonals: T(n,k) = T(n,k-1) + T(n,k-2) where T(n,0) = F(n+1), T(n,1) = F(n); F(n) = Fibonacci(n) = A000045(n).
A271315 0 SD Array T(n,k) read by diagonals: T(n,k) = T(n,k-1) + T(n,k-2) where T(n,0) = F(n+1), T(n,1) = F(n); F(n) = Fibonacci(n) = A000045(n).