A222082 Self-convolution square of A090845.

1, 2, 5, 10, 20, 40, 67, 126, 203, 354, 571, 908, 1486, 2250, 3586, 5322, 8186, 12234, 17976, 26970, 38435, 57024, 80805, 116376, 165914, 232352, 332196, 456154, 645469, 885826, 1225998, 1692686, 2290512, 3168986, 4242896, 5805526, 7782803, 10459912, 14110205

Offset: 0

Author

Paul D. Hanna, Feb 06 2013

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 2*x + 5*x^2 + 10*x^3 + 20*x^4 + 40*x^5 + 67*x^6 +...
Let G(x) = A(x)^(1/2) denote the g.f. of A090845:
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 +...
then the coefficients of G(x)^2 and G(x)^3 begin:
G(x)^2: [1, 2, 5, 10, 20, 40, 67, 126, 203, 354, 571, 908, 1486, ...];
G(x)^3: [1, 3, 9, 22, 51, 114, 230, 468, 885, 1674, 3045, 5418, ..];
where the sorted union of these coefficients yield sequence A090845.
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A090845, A222083.

Programs

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]}
for(n=0, 60, print1(a(n), ", "))