The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A173747 Square array T(n, k) = v(k, n)((1)), where v(n, q) = M*v(n-1, q), M = {{0, 1, 0}, {0, 0, 1}, {8*q^3, 6*q, 0}}, with v(0, q) = {1, 1, 1}, read by antidiagonals. 4
 1, 1, 1, 1, 1, 1, 14, 1, 1, 1, 14, 76, 1, 1, 1, 92, 76, 234, 1, 1, 1, 196, 976, 234, 536, 1, 1, 1, 664, 5776, 4428, 536, 1030, 1, 1, 1, 1912, 16576, 54756, 13376, 1030, 1764, 1, 1, 1, 5552, 131776, 130248, 287296, 31900, 1764, 2786, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 LINKS G. C. Greubel, Antidiagonal rows n = 0..50, flattened FORMULA T(n, k) = v(k, n)((1)), where v(n, q) = M*v(n-1, q), M = {{0, 1, 0}, {0, 0, 1}, {8*q^3, 6*q, 0}}, with v(0, q) = {1, 1, 1} (square array). T(n, k) = f(k, n+1), where f(n, q) = 6*q*f(n-2, q) + 8*q^3*f(n-3, q), and f(0,q) = f(1,q) = f(2,q) = 1 (square array). - G. C. Greubel, Jul 06 2021 EXAMPLE Square array begins as: 1, 1, 1, 14, 14, 92, ...; 1, 1, 1, 76, 76, 976, ...; 1, 1, 1, 234, 234, 4428, ...; 1, 1, 1, 536, 536, 13376, ...; 1, 1, 1, 1030, 1030, 31900, ...; 1, 1, 1, 1764, 1764, 65232, ...; Antidiagonal triangle begins as: 1; 1, 1; 1, 1, 1; 14, 1, 1, 1; 14, 76, 1, 1, 1; 92, 76, 234, 1, 1, 1; 196, 976, 234, 536, 1, 1, 1; 664, 5776, 4428, 536, 1030, 1, 1, 1; 1912, 16576, 54756, 13376, 1030, 1764, 1, 1, 1; 5552, 131776, 130248, 287296, 31900, 1764, 2786, 1, 1, 1; MATHEMATICA (* First program *) M = {{0, 1, 0}, {0, 0, 1}, {8*q^3, 6*q, 0}}; v[0, q_] = {1, 1, 1}; v[n_, q_]:= v[n, q]= M.v[n-1, q]; T = Table[v[n, q][[1]], {n, 0, 20}, {q, 1, 21}]; Table[T[[n-k+1, k+1]], {n, 0, 10}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Jul 06 2021 *) (* Second program *) f[n_, q_]:= f[n, q]= If[n<3, 1, 6*q*f[n-2, q] + 8*q^3*f[n-3, q]]; T[n_, k_]:= f[k, n+1]; Table[T[k, n-k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Jul 06 2021 *) PROG (Sage) @CachedFunction def f(n, q): return 1 if (n<3) else 6*q*f(n-2, q) + 8*q^3*f(n-3, q) def T(n, k): return f(k, n+1) flatten([[T(k, n-k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jul 06 2021 CROSSREFS Cf. A173749, A173778, A173779. Sequence in context: A262705 A232210 A040199 * A040200 A040198 A040197 Adjacent sequences: A173744 A173745 A173746 * A173748 A173749 A173750 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Feb 23 2010 EXTENSIONS Edited by G. C. Greubel, Jul 06 2021 STATUS approved

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

Last modified May 24 12:09 EDT 2024. Contains 372773 sequences. (Running on oeis4.)