The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A126331 Triangle T(n,k), 0 <= k <= n, read by rows defined by: T(0,0)=1, T(n,k)=0 if k < 0 or if k > n, T(n,0) = 4*T(n-1,0) + T(n-1,1), T(n,k) = T(n-1,k-1) + 5*T(n-1,k) + T(n-1,k+1) for k >= 1. 25
 1, 4, 1, 17, 9, 1, 77, 63, 14, 1, 371, 406, 134, 19, 1, 1890, 2535, 1095, 230, 24, 1, 10095, 15660, 8240, 2269, 351, 29, 1, 56040, 96635, 59129, 19936, 4053, 497, 34, 1, 320795, 598344, 412216, 162862, 40698, 6572, 668, 39, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This triangle belongs to the family of triangles defined by: T(0,0)=1, T(n,k)=0 if k < 0 or if k > n, T(n,0) = x*T(n-1,0) + T(n-1,1), T(n,k) = T(n-1,k-1) + y*T(n-1,k) + T(n-1,k+1) for k >= 1. Other triangles arise from choosing different values for (x,y): (0,0) -> A053121; (0,1) -> A089942; (0,2) -> A126093; (0,3) -> A126970; (1,0)-> A061554; (1,1) -> A064189; (1,2) -> A039599; (1,3) -> A110877; (1,4) -> A124576; (2,0) -> A126075; (2,1) -> A038622; (2,2) -> A039598; (2,3) -> A124733; (2,4) -> A124575; (3,0) -> A126953; (3,1) -> A126954; (3,2) -> A111418; (3,3) -> A091965; (3,4) -> A124574; (4,3) -> A126791; (4,4) -> A052179; (4,5) -> A126331; (5,5) -> A125906. - Philippe Deléham, Sep 25 2007 7^n = (n-th row terms) dot (first n+1 odd integers). Example: 7^3 = 343 = (77, 63, 14, 1) dot (1, 3, 5, 7) = (77 + 189 + 70 + 7) = 243. - Gary W. Adamson, Jun 15 2011 LINKS G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened FORMULA Sum_{k=0..n} T(n,k) = A098409(n). Sum_{k>=0} T(m,k)*T(n,k) = T(m+n,0) = A104455(m+n). Sum_{k=0..n} T(n,k)*(2*k+1) = 7^n. - Philippe Deléham, Mar 26 2007 EXAMPLE Triangle begins:       1;       4,     1;      17,     9,    1;      77,    63,   14,    1;     371,   406,  134,   19,   1;    1890,  2535, 1095,  230,  24,  1;   10095, 15660, 8240, 2269, 351, 29, 1; From Philippe Deléham, Nov 07 2011: (Start) Production matrix begins:   4, 1   1, 5, 1   0, 1, 5, 1   0, 0, 1, 5, 1   0, 0, 0, 1, 5, 1,   0, 0, 0, 0, 1, 5, 1   0, 0, 0, 0, 0, 1, 5, 1   0, 0, 0, 0, 0, 0, 1, 5, 1   0, 0, 0, 0, 0, 0, 0, 1, 5, 1 (End) MATHEMATICA T[0, 0, x_, y_] := 1; T[n_, 0, x_, y_] := x*T[n - 1, 0, x, y] + T[n - 1, 1, x, y]; T[n_, k_, x_, y_] := T[n, k, x, y] = If[k < 0 || k > n, 0, T[n - 1, k - 1, x, y] + y*T[n - 1, k, x, y] + T[n - 1, k + 1, x, y]]; Table[T[n, k, 4, 5], {n, 0, 10}, {k, 0, n}] // Flatten (* G. C. Greubel, May 22 2017 *) CROSSREFS Sequence in context: A126791 A052179 A171589 * A013631 A331651 A113355 Adjacent sequences:  A126328 A126329 A126330 * A126332 A126333 A126334 KEYWORD nonn,tabl AUTHOR Philippe Deléham, Mar 10 2007 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 May 31 02:51 EDT 2020. Contains 334747 sequences. (Running on oeis4.)