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A222082 Self-convolution square of A090845.

%I A222082 #4 Feb 06 2013 22:46:24
%S A222082 1,2,5,10,20,40,67,126,203,354,571,908,1486,2250,3586,5322,8186,12234,
%T A222082 17976,26970,38435,57024,80805,116376,165914,232352,332196,456154,
%U A222082 645469,885826,1225998,1692686,2290512,3168986,4242896,5805526,7782803,10459912,14110205
%N A222082 Self-convolution square of A090845.
%H A222082 Paul D. Hanna, <a href="/A222082/b222082.txt">Table of n, a(n) for n = 0..10000</a>
%e A222082 G.f.: A(x) = 1 + 2*x + 5*x^2 + 10*x^3 + 20*x^4 + 40*x^5 + 67*x^6 +...
%e A222082 Let G(x) = A(x)^(1/2) denote the g.f. of A090845:
%e A222082 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 A222082 then the coefficients of G(x)^2 and G(x)^3 begin:
%e A222082 G(x)^2: [1, 2, 5, 10, 20, 40, 67, 126, 203, 354, 571, 908, 1486, ...];
%e A222082 G(x)^3: [1, 3, 9, 22, 51, 114, 230, 468, 885, 1674, 3045, 5418, ..];
%e A222082 where the sorted union of these coefficients yield sequence A090845.
%o A222082 (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)^2)[n+1]}
%o A222082 for(n=0, 60, print1(a(n), ", "))
%Y A222082 Cf. A090845, A222083.
%K A222082 nonn
%O A222082 0,2
%A A222082 _Paul D. Hanna_, Feb 06 2013