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A222083 Self-convolution cube of A090845.

%I A222083 #4 Feb 06 2013 22:49:52
%S A222083 1,3,9,22,51,114,230,468,885,1674,3045,5418,9560,16341,27912,46383,
%T A222083 76794,125205,201580,322980,508710,800495,1241190,1916682,2935492,
%U A222083 4456617,6747393,10101532,15105042,22378362,33035166,48520809,70776711,103072393,148899756
%N A222083 Self-convolution cube of A090845.
%C A222083 A090846 gives the positions of where the terms of this sequence are found in A090845.
%H A222083 Paul D. Hanna, <a href="/A222083/b222083.txt">Table of n, a(n) for n = 0..10000</a>
%e A222083 G.f.: A(x) = 1 + 3*x + 9*x^2 + 22*x^3 + 51*x^4 + 114*x^5 + 230*x^6 +...
%e A222083 Let G(x) = A(x)^(1/3)  denote the g.f. of A090845:
%e A222083 G(x) = 1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 9*x^5 + 10*x^6 + 20*x^7 + 22*x^8 + 40*x^9 + 51*x^10 + 67*x^11 + 114*x^12 + 126*x^13 + 203*x^14 +...
%e A222083 then the coefficients of G(x)^2 and G(x)^3 begin:
%e A222083 G(x)^2: [1, 2, 5, 10, 20, 40, 67, 126, 203, 354, 571, 908, 1486, ...];
%e A222083 G(x)^3: [1, 3, 9, 22, 51, 114, 230, 468, 885, 1674, 3045, 5418, ..];
%e A222083 where the sorted union of these coefficients yield sequence A090845.
%o A222083 (PARI) {a(n)=local(A=[1, 1]); for(i=1, #binary(3*n+1), A=vecsort(concat(Vec(Ser(A)^2), Vec(Ser(A)^3)))); Vec(Ser(A)^3)[n+1]}
%o A222083 for(n=0, 60, print1(a(n), ", "))
%Y A222083 Cf. A090845, A090846, A222082.
%K A222083 nonn
%O A222083 0,2
%A A222083 _Paul D. Hanna_, Feb 06 2013