A147982 Expansion of Product_{k > 0} (1 + f(k)*x^k), where f(k) = A147952(A004001(k)).

1, 1, 1, 2, 2, 4, 6, 8, 11, 16, 20, 28, 38, 50, 69, 92, 120, 154, 203, 261, 338, 437, 559, 710, 907, 1146, 1444, 1829, 2291, 2863, 3593, 4457, 5539, 6882, 8503, 10501, 12931, 15861, 19466, 23854, 29125, 35520, 43279, 52557, 63735, 77358, 93472, 112885

Offset

0,4

Links

Table of n, a(n) for n=0..47.

Formula

a(n) = [x^n] Product_{k > 0} (1 + f(k)*x^k), where f(k) = A147952(A004001(k)).

Mathematica

(* A004001 *) g[0] = 0; g[1] = 1; g[2] = 1; g[n_] := g[n] = g[g[n - 1]] + g[n - g[n - 1]];
(*A147952*) f[0] = 0; f[1] = 1; f[2] = 1; f[n_] := f[n] = f[f[n - 2]] + If[Mod[n, 3] == 0, f[f[n/3]], If[Mod[n, 3] ==1, f[f[(n - 1)/3]], f[n - f[(n - 2)/3]]]];
P[x_, n_] := P[x, n] = Product[1 + f[g[m]]*x^m, {m, 0, n}];
Take[CoefficientList[P[x, 45], x], 45] (* Program simplified and corrected by Petros Hadjicostas, Apr 11 2020 using code from A147869 *)

Crossrefs

Cf. A004001, A147869, A147952.

Sequence in context: A241383 A258125 A361394 * A329899 A051466 A320193

Adjacent sequences: A147979 A147980 A147981 * A147983 A147984 A147985

Keyword

nonn

Author

Roger L. Bagula, Nov 18 2008

Extensions

Various sections edited by Petros Hadjicostas, Apr 11 2020

Status

approved