A147953 Expansion of Product_{k > 0} (1 + f(k)*x^k), where f(n) = A147952(n).

1, 1, 1, 3, 4, 7, 9, 14, 22, 32, 43, 61, 89, 118, 167, 235, 312, 417, 572, 748, 1006, 1326, 1744, 2283, 2982, 3878, 5048, 6518, 8355, 10786, 13727, 17436, 22173, 28250, 35561, 45008, 56651, 70818, 88992, 111280, 138431, 172284, 214019, 265166, 328127

Offset

0,4

Links

Table of n, a(n) for n=0..44.

Formula

a(n) = [x^n] Product_{k > 0} (1 + f(k)*x^k), where f(1) = f(2) = 1, and for m >= 3, f(m) = f(f(m-2)) + r(m), where r(m) = f(f(floor(m/3)) when m == 0 or 1 (mod 3) and = f(m - f(floor(m/3))) when m == 2 (mod 3).

Mathematica

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[m] x^m, {m, 0, n}];
Take[CoefficientList[P[x, 45], x], 45]
(* Program edited and corrected by Petros Hadjicostas, Apr 12 2020 *)

Crossrefs

Cf. A147654, A147655, A147665, A147869, A147871, A147880, A147952.

Sequence in context: A008763 A349795 A005896 * A163468 A069183 A119907

Adjacent sequences: A147950 A147951 A147952 * A147954 A147955 A147956

Keyword

nonn

Author

Roger L. Bagula, Nov 17 2008

Extensions

Various sections edited by Petros Hadjicostas, Apr 12 2020

Status

approved