A147953 - OEIS

%I #35 Apr 14 2020 01:11:53

%S 1,1,1,3,4,7,9,14,22,32,43,61,89,118,167,235,312,417,572,748,1006,

%T 1326,1744,2283,2982,3878,5048,6518,8355,10786,13727,17436,22173,

%U 28250,35561,45008,56651,70818,88992,111280,138431,172284,214019,265166,328127

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

%F 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).

%t f[0] = 0; f[1] = 1; f[2] = 1;

%t 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]]]];

%t P[x_, n_] := P[x, n] = Product[1 + f[m] x^m, {m, 0, n}];

%t Take[CoefficientList[P[x, 45], x],45]

%t (* Program edited and corrected by _Petros Hadjicostas_, Apr 12 2020 *)

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

%K nonn

%O 0,4

%A _Roger L. Bagula_, Nov 17 2008

%E Various sections edited by _Petros Hadjicostas_, Apr 12 2020