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Triangles Row Sum Fibonacci
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Fibonacci numbers
A026729 Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by antidiagonals.
A030528 Triangle read by rows: a(n,k) = binomial(k,n-k).
A039961 Triangle of coefficients in a Fibonacci-like sequence of polynomials.
A046854 Triangle in which k-th entry of row n is binomial(floor(n/2+k/2),k), n>=0, n >= k >= 0.
A049310 Triangle of coefficients of Chebyshev's S(n,x) := U(n,x/2) polynomials (exponents in increasing order).
A052553 Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by antidiagonals.
A053119 Triangle of coefficients of Chebyshev's S(n,x) polynomials (exponents in decreasing order).
A054123 Right Fibonacci row-sum array T(n,k), n >= 0, 0<=k<=n.
A054124 Left Fibonacci row-sum array, n >= 0, 0<=k<=n.
A057094 Coefficient triangle for certain polynomials (rising powers).
A065941 Triangle T(n,k) = binomial(n-floor((k+1)/2), floor(k/2)).
A066170 Triangle read by rows: T(n,k) = (-1)^n*(-1)^(floor(3*k/2))*binomial(floor((n+k)/2),k), 0<=k<=n , n>=0.
A073044 Triangle read by rows: T(n,k) (n>=1, n-1>=k>=0) = number of n-sequences of 0's and 1's with no pair of adjacent 0's and exactly k pairs of adjacent 1's.
A078808 Triangular array T given by T(n,k) = number of 01-words of length n having exactly k 1's, all runlengths odd and first letter 1.
A079487 Triangle read by rows giving Whitney numbers T(n,k) of Fibonacci lattices.
A103631 Triangle read by rows: an invertible triangle whose row sums are F(n+1).
A108299 Triangle read by rows, 0 <= k <= n: T(n,k) = binomial(n-[(k+1)/2],[k/2])*(-1)^[(k+1)/2].
A109466 Riordan array (1, x(1-x)).
A123245 Triangle A079487 with reversed rows.
A127647 Triangle read by rows: row n consists of n-1 zeros followed by Fibonacci(n).
A129713 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.
A129714 Triangle read by rows: T(n,k) is the number of Fibonacci binary words of length n and having k runs (0<=k<=n). A Fibonacci binary word is a binary word having no 00 subword. A run is a maximal sequence of consecutive identical letters.
A130116 Inverse Moebius transform of a diagonalized matrix of A007436.
A130777 Coefficients of first difference of Chebyshev S polynomials.
A131334 A000012(signed) * A065941.
A133607 Triangle T(n,k), 0<=k<=n, read by rows given by [0, 1, 0, 0, 0, 0, 0, 0, 0, ...] DELTA [1, -2, 1, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938 .
A144152 Eigentriangle, row sums = Fibonacci numbers.
A144961 Eigentriangle whose left border is the Padovan sequence, and whose right border and row sums are a modified Fibonacci sequence.
A153764 Triangle T(n,k), 0<=k<=n, read by rows, given by [1,0,-1,0,0,0,0,0,0,0,0,...] DELTA [0,1,0,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938 .
A168561 Riordan array (1/(1-x^2), x/(1-x^2)). Unsigned version of A049310.
A169803 Triangle read by rows: T(n,k) = binomial(n+1-k,k) (n >= 0, 0 <= k <= n).
A178524 Triangle read by rows: T(n,k) is the number of leaves at level k in the Fibonacci tree of order n (n>=0, 0<=k<=n-1).
A187660 Triangle in which T(n,k) = (-1)^(floor[3*k/2])*binomial[floor[(n+k)/2],k] is entry k of row n, where 0<=k<=n.
A192575 Triangle T(n,0) = A040000(n), T(n,k)=0 (odd-numbered columns); T(n,k) = (-1)^(k/2)*A110813(n-k/2-1,k/2-1) (even-numbered columns, k>0).
A216226 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=1 or if k-n>=4, T(0,0) = T(0,1) = T(0,2) = T(0,3) = 1, T(n,k) = T(n-1,k) + T(n,k-1).
A216229 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=2 or if k-n>=3, T(1,0) = T(0,0) = T(0,1) = T(0,2) = 1, T(n,k) = T(n-1,k) + T(n,k-1).
A238160 A skewed version of triangular array A029653.
A242086 Triangle read by rows: T(n,k) is the number of compositions of n into odd parts with first part k.
A245825 Triangle read by rows: T(n,k) is the number of the vertices of the Fibonacci cube G_n that have degree k (0<=k<=n).
A267482 Triangle of coefficients of Gaussian polynomials [2n+1,1]_q represented as finite sum of terms (1+q^2)^k*q^(g-k), where k = 0,1,...,g with g=n.
Fibonacci(2n)
A049600 Array T read by diagonals; T(i,j)=number of paths from (0,0) to (i,j) consisting of nonvertical segments (x(k),y(k))-to-(x(k+1),y(k+1)) such that 0=x(1)<x(2)<...<x(n-1)<x(n)=i, 0=y(1)<=y(2)<=...y(n-1)<=y(n)=j, for i >= 0, j >= 0.
A053122 Triangle of coefficients of Chebyshev's S(n,x-2)= U(n,x/2-1) polynomials (exponents of x in increasing order).
A053123 Triangle of coefficients of shifted Chebyshev's S(n,x-2)= U(n,x/2-1) polynomials (exponents of x in decreasing order).
A054134 Even-index Fibonacci row-sum array: T(n,0)=U(2n,n)/2, T(n,k)=U(2n,n+k) for k=1,2,...,n, n >= 0, U the array in A054125.
A055587 Triangle with columns built from row sums of the partial row sums triangles obtained from Pascal's triangle A007318. Essentially A049600 formatted differently.
A071920 Square array giving number of unimodal functions [n]->[m] for n>=0, m>=0, with a(0,m)=0 for all m>=0, read by antidiagonals.
A078812 Triangle read by rows: T(n, k) = binomial(n+k-1, 2*k-1).
A094435 Triangular array read by rows: T(n,k)=F(k)C(n,k), k=1,2,3,...,n; n>=1.
A094437 Triangular array T(n,k)=F(k+2)C(n,k), k=0,1,2,3,...,n; n>=0.
A094439 Triangular array T(n,k)=F(k+4)C(n,k), k=0,1,2,3,...,n; n>=0.
A094440 Triangular array T(n,k) = F(n+1-k)*C(n,k-1), k = 1,2,3,...,n; n >= 1.
A094442 Triangular array T(n,k)=F(n+2-k)C(n,k), 0<=k<=n.
A094444 Triangular array T(n,k)=F(n+4-k)C(n,k), k=0,1,2,...,n; n>=0.
A106195 Riordan array (1/(1-2x),x(1-x)/(1-2x)).
A113020 Number triangle whose row sums are the Fibonacci numbers.
A121464 Triangle read by rows: T(n,k) is the number of nondecreasing Dyck paths of semilength n, having k triangles (0<=k<=n). A triangle in a Dyck path is a subpath of the form U^h D^h, starting at the x-axis; here U=(1,1), D=(1,-1), h being the height of the triangle.
A128908 Riordan array (1,x/(1-x)^2).
A140069 Triangle read by rows, n-th row = (n-1)-th power of the matrix X * [1,0,0,0,...]; where X = an infinite lower triangular bidiagonal matrix with [2,1,2,1,2,1,...] and [1,1,1,...] in the subdiagonal.
A143929 Eigentriangle by rows, termwise products of the natural numbers decrescendo and the bisected Fibonacci series.
A144224 T(n,k) is the number of idempotent order-preserving full transformations (of an n-element chain) of waist k (waist(alpha) = max(Im(alpha))).
A171731 Triangle T : T(n,k)= binomial(n,k)*Fibonacci(n-k)= A007318(n,k)*A000045(n-k).
A172431 Even row Pascal-square read by anti-diagonals.
A175011 Triangle read by rows, antidiagonals of an array generated from INVERT transforms of variants of (1, 2, 3,...).
A180339 Triangle by rows, A137710 * a diagonalized variant of A001906
A207607 Triangle of coefficients of polynomials v(n,x) jointly generated with A207606; see Formula section.
A208341 Triangle read by rows, T(n,k) = hypergeometric_2F1([n-k+1, -k], [1], -1) for n>=0 and k>=0.
A208345 Triangle of coefficients of polynomials v(n,x) jointly generated with A208344; see the Formula section.
A209413 Triangle of coefficients of polynomials v(n,x) jointly generated with A209172; see the Formula section.
A210211 Triangle of coefficients of polynomials u(n,x) jointly generated with A210212; see the Formula section.
A210213 Triangle of coefficients of polynomials u(n,x) jointly generated with A210214; see the Formula section.
A210217 Triangle of coefficients of polynomials u(n,x) jointly generated with A210218; see the Formula section.
A210219 Triangle of coefficients of polynomials u(n,x) jointly generated with A210220; see the Formula section.
A210549 Triangle of coefficients of polynomials u(n,x) jointly generated with A210550; see the Formula section.
A210596 Triangle of coefficients of polynomials v(n,x) jointly generated with A210221; see the Formula section.
A213947 Triangle read by rows: columns are finite differences of the INVERT transform of (1, 2, 3,...) terms
Fibonacci(2n+1) : A001519
A050143 Array T by antidiagonals: T(i,j)=Sum{T(h,k): 0<=h<=i-1, 0<=k<=j}, T(i,0)=1 for i >= 0, T(0,j)=0 for j >= 1.
A054126 Odd-index Fibonacci row-sum array: T(n,k)=U(2n+1,n+1+k), 0<=k<=n, n >= 0, U the array in A054125.
A054142 Triangular array C(2n-k,k), k=0,1,...,n, n >= 0.
A055807 Array T read by rows: T(i,j)=R(i-j,j), where R(i,0)=1 for i >= 0, R(0,j)=0 for j >= 1, R(i,j)=Sum{R(h,k): 0<=h<=i-1, 0<=k<=j} for i >= 1, j >= 1.
A062110 Table read by antidiagonals where T(n,k) is coefficient of x^k in (1-x)^n/(1-2x)^n.
A076756 Triangle of coefficients of characteristic polynomial of M_n, the n X n matrix M_(i,j) = min(i,j).
A085478 Triangle read by rows: T(n, k) = binomial(n + k, 2*k).
A094436 Triangular array T(n,k) = F(k+1)C(n,k), k=0,1,2,3,...,n; n>=0.
A094438 Triangular array T(n,k)=F(k+3)C(n,k), k=0,1,2,3,...,n; n>=0.
A094441 Triangular array T(n,k)=F(n+1-k)C(n,k), 0<=k<=n.
A094443 Triangular array T(n,k)=F(n+3-k)C(n,k), k=0,1,2,...,n; n>=0.
A105292 Triangle read by rows: T(n,k) is the number of directed column-convex polyominoes of area n, having leftmost column of height k.
A105306 Triangle read by rows: T(n,k) is the number of directed column-convex polyominoes of area n, having the top of the rightmost column at height k.
A105929 Triangle read by rows: T(n,k) is the number of directed column-convex polyominoes of area n, having k columns of height 1 starting at level 0.
A110438 Triangular array giving the number of NSEW unit step lattice paths of length n with terminal height k subject to the following restrictions. The paths start at the origin (0,0) and take unit steps (0,1)=N(north), (0,-1)=S(south), (1,0)=E(east) and (-1,0)=W(west) such that no paths pass below the x-axis, no paths begin with W, all W steps remain on the x-axis and there are no NS steps.
A121298 Triangle read by rows: T(n,k) is the number of directed column-convex polyominoes of area n and height k (1<=k<=n; here by the height of a polyomino one means the number of lines of slope -1 that pass through the centers of the polyomino cells).
A121300 Triangle read by rows: T(n,k) is the number of directed column-convex polyominoes of area n and having k cells in the longest column (1<=k<=n).
A121301 Triangle read by rows: T(n,k) is the number of directed column-convex polyominoes of area n and having k cells in the shortest column (1<=k<=n).
A121314 Triangle T(n,k), 0<=k<=n, read by rows given by [0, 1, 0, 0, 0, 0, ...] DELTA [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938.
A121460 Triangle read by rows: T(n,k) is the number of nondecreasing Dyck paths of semilength n, having k returns to the x-axis (1<=k<=n).
A121461 Triangle read by rows: T(n,k) is the number of nondecreasing Dyck paths of semilength n, having last ascent of length k (1<=k<=n).
A121462 Triangle read by rows: T(n,k) is the number of nondecreasing Dyck paths of semilength n, having pyramid weight k (1<=k<=n).
A121464 Triangle read by rows: T(n,k) is the number of nondecreasing Dyck paths of semilength n, having k triangles (0<=k<=n). A triangle in a Dyck path is a subpath of the form U^h D^h, starting at the x-axis; here U=(1,1), D=(1,-1), h being the height of the triangle.
A121465 Triangle read by rows: T(n,k) is the number of nondecreasing Dyck paths of semilength n such that the sum of the heights of their triangles is k (0<=k<=n). A triangle in a Dyck path is a subpath of the form U^h D^h, starting at the x-axis; here U=(1,1), D=(1,-1), h being the height of the triangle.
A121469 Triangle read by rows: T(n,k) is the number of directed column-convex polyominoes of area n having k 1-cell columns (0<=k<=n).
A121481 Triangle read by rows: T(n,k) is the number of nondecreasing Dyck paths of semilength n, having k peaks at odd level (0<=k<=n).
A121484 Triangle read by rows: T(n,k) is the number of nondecreasing Dyck paths of semilength n, having k peaks at even level (n>=1,0<=k<=n-1). A nondecreasing Dyck path is a Dyck path for which the sequence of the altitudes of the valleys is nondecreasing.
A121487 Triangle read by rows: T(n,k) is the number of nondecreasing Dyck paths of semilength n and having abscissa of first return equal to 2k (1<=k<=n). A nondecreasing Dyck path is a Dyck path for which the sequence of the altitudes of the valleys is nondecreasing.
A121522 Triangle read by rows: T(n,k) is the number of nondecreasing Dyck paths of semilength n and having k up steps starting at an even level (1<=k<=n). A nondecreasing Dyck path is a Dyck path for which the sequence of the altitudes of the valleys is nondecreasing.
A121524 Triangle read by rows: T(n,k) is the number of nondecreasing Dyck paths of semilength n and having k up steps starting at an odd level (0<=k<=n-1). A nondecreasing Dyck path is a Dyck path for which the sequence of the altitudes of the valleys is nondecreasing.
A123970 Triangle read by rows: T(0,0)=1; T(n,k) is the coefficient of x^(n-k) in the monic characteristic polynomial of the n X n matrix (min(i,j)) (i,j=1,2,...n) (0<=k<=n, n>=1).
A124802 Triangle, row sums = Fibonacci numbers in two ways, companion to A124801.
A129818 Riordan array (1/(1+x),x/(1+x)^2), inverse array is A039599.
A140068 Triangle read by rows, n-th row = (n-1)-th power of the matrix X * [1,0,0,0,...] where X = an infinite lower triangular matrix with [1,2,1,2,1,2,...] in the main diagonal and [1,1,1,...] in the subdiagonal.
A144224 T(n,k) is the number of idempotent order-preserving full transformations (of an n-element chain) of waist k (waist(alpha) = max(Im(alpha))).
A152251 Eigentriangle, row sums = A001519, odd-indexed Fibonacci numbers.
A153342 Binomial transform of triangle A046854 (shifted).
A160232 Array read by antidiagonals: row n has g.f. ((1-x)/(1-2x))^n.
A165253 Triangle T(n,k), read by rows given by [1,0,1,0,0,0,0,0,0,...] DELTA [0,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938 .
A179745 Triangle read by rows,derived from iterates of operations in which a current eigensequence becomes the left border of a new triangle; with triangles of the form: all 1's except the left border for triangles >1.
A188285 Riordan matrix ( (1-2x)/(1-2x-x^2}, (x-2x^2)/(1-2x-x^2) ).
A202672 Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of the symmetric matrix A087062 based on (1,1,1,1,...); by antidiagonals.
A207606 Triangle of coefficients of polynomials u(n,x) jointly generated with A207607; see the Formula section.
A208344 Triangle of coefficients of polynomials u(n,x) jointly generated with A208345; see the Formula section.
A209172 Triangle of coefficients of polynomials u(n,x) jointly generated with A209413; see the Formula section.
A213948 Triangle, by rows, generated from the INVERT transforms of (1, 1, 2, 4, 8, 16,...)
A238156 Triangle T(n,k), 0<=k<=n, read by rows, given by (0, 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.
Fibonacci(3n)
A125077 #4 in an infinite set of generalized Pascal's triangles with trigonometric properties.
A137509 a(1)=2. For n >= 2, a(n) = the smallest integer > a(n-1) that has the same multiset of prime-factorization exponents as n has.
A178442 Two numbers k and l we call equivalent if they have the same vector of exponents with positive components in prime power factorization. Let a(1)=1, a(2)=3. Then a(n)>a(n-1) is the smallest number equivalent to n.
A180063 Pascal-like triangle with trigonometric properties, row sums = powers of 4; generated from shifted columns of triangle A180062.
A195587 a(n) = A163659(n^2), where A163659 is the logarithmic derivative of Stern's diatomic series (A002487).
partial match
A058661 McKay-Thompson series of class 39C for Monster.
A094362 McKay-Thompson series of class 39C for the Monster group with a(0) = 1.
Fibonacci(3n+1)
A122070 Triangle T(n,k), 0<=k<=n, given by T(n,k)=Fibonacci(n+k+1)*binomial(n,k).
A185384 A binomial transform of Fibonacci numbers.
