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

%I A147982 #19 Apr 14 2020 03:31:35
%S A147982 1,1,1,2,2,4,6,8,11,16,20,28,38,50,69,92,120,154,203,261,338,437,559,
%T A147982 710,907,1146,1444,1829,2291,2863,3593,4457,5539,6882,8503,10501,
%U A147982 12931,15861,19466,23854,29125,35520,43279,52557,63735,77358,93472,112885
%N A147982 Expansion of Product_{k > 0} (1 + f(k)*x^k), where f(k) = A147952(A004001(k)).
%F A147982 a(n) = [x^n] Product_{k > 0} (1 + f(k)*x^k), where f(k) = A147952(A004001(k)).
%t A147982 (* A004001 *) g[0] = 0; g[1] = 1; g[2] = 1; g[n_] := g[n] = g[g[n - 1]] + g[n - g[n - 1]];
%t A147982 (*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]]]];
%t A147982 P[x_, n_] := P[x, n] = Product[1 + f[g[m]]*x^m, {m, 0, n}];
%t A147982 Take[CoefficientList[P[x, 45], x], 45] (* Program simplified and corrected by _Petros Hadjicostas_, Apr 11 2020 using code from A147869 *)
%Y A147982 Cf. A004001, A147869, A147952.
%K A147982 nonn
%O A147982 0,4
%A A147982 _Roger L. Bagula_, Nov 18 2008
%E A147982 Various sections edited by _Petros Hadjicostas_, Apr 11 2020