This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A073387 Convolution triangle of A002605(n) (generalized (2,2)-Fibonacci), n>=0. 16
 1, 2, 1, 6, 4, 1, 16, 16, 6, 1, 44, 56, 30, 8, 1, 120, 188, 128, 48, 10, 1, 328, 608, 504, 240, 70, 12, 1, 896, 1920, 1872, 1080, 400, 96, 14, 1, 2448, 5952, 6672, 4512, 2020, 616, 126, 16, 1, 6688, 18192, 23040, 17856, 9352, 3444, 896, 160, 18, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The g.f. for the row polynomials P(n,x) := Sum_{m=0..n} a(n,m)*x^m is 1/(1-(2+x+2*z)*z). See Shapiro et al. reference and comment under A053121 for such convolution triangles. The column sequences (without leading zeros) give A002605, A073388-94, A073397-8 for m=0..9. Row sums give A007482. T(n,k) is the number of words of length n over {0,1,2,3} having k letters 3 and avoiding runs of odd length for the letters 0,1. - Milan Janjic, Jan 14 2017 LINKS W. Lang, First 10 rows. FORMULA a(n, m) = 2*(p(m-1, n-m)*(n-m+1)*a(n-m+1) + q(m-1, n-m)*(n-m+2)*a(n-m))/(m!*12^m), n>=m>=1, with a(n)=a(n, m=0) := A002605(n), else 0; p(k, n) := Sum_{l=0..k} A(k, l)*n^(k-l) and q(k, n) := Sum_{l=0..k} B(k, l)*n^(k-l) with the number triangles A(k, m) := A073403(k, m) and B(k, m) := A073404(k, m). a(n, m) = Sum_{k=0..floor((n-m)/2)} ((2^(n-m))*binomial(n-k, m)*binomial(n-m-k, k)*(1/2)^k) if n>m, else 0. a(n, m) = ((n-m+1)*a(n, m-1) + 2*(n+m)*a(n-1, m-1))/(6*m), n >= m >= 1, a(n, 0) = A002605(n+1), else 0. G.f. for column m (without leading zeros): 1/(1-2*x*(1+x))^(m+1), m>=0. T(n,k) = 2^(n-k)*binomial(n,k)*hypergeom([(k-n)/2, (k-n+1)/2], [-n], -2)) for n>=1. - Peter Luschny, Apr 25 2016 EXAMPLE Lower triangular matrix a(n,m), n >= m >= 0, else 0:     {1},     {2,   1},     {6,   4,   1},    {16,  16,   6,   1},    {44,  56,  30,   8,   1},   {120, 188, 128,  48,  10,   1},   {328, 608, 504, 240,  70,  12,   1},   ... MAPLE T := (n, k) -> `if`(n=0, 1, 2^(n-k)*binomial(n, k)*hypergeom([(k-n)/2, (k-n+1)/2], [-n], -2)): seq(seq(simplify(T(n, k)), k=0..n), n=0..10); # Peter Luschny, Apr 25 2016 MATHEMATICA a[n_, m_] := Sum[2^(n-m)*Binomial[n-k, m]*Binomial[n-m-k, k]*(1/2)^k, {k, 0, (n-m)/2}]; Table[a[n, m], {n, 0, 9}, {m, 0, n}] // Flatten (* Jean-François Alcover, Jun 04 2019 *) CROSSREFS Cf. A002605, A053121, A073403, A073404. Sequence in context: A269505 A269479 A118040 * A259099 A125693 A094527 Adjacent sequences:  A073384 A073385 A073386 * A073388 A073389 A073390 KEYWORD nonn,easy,tabl AUTHOR Wolfdieter Lang, Aug 02 2002 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 22 10:03 EDT 2019. Contains 325219 sequences. (Running on oeis4.)