A222083 Self-convolution cube of A090845.

1, 3, 9, 22, 51, 114, 230, 468, 885, 1674, 3045, 5418, 9560, 16341, 27912, 46383, 76794, 125205, 201580, 322980, 508710, 800495, 1241190, 1916682, 2935492, 4456617, 6747393, 10101532, 15105042, 22378362, 33035166, 48520809, 70776711, 103072393, 148899756

Offset: 0

Author

Paul D. Hanna, Feb 06 2013

Keywords

• nonn

Comments

A090846 gives the positions of where the terms of this sequence are found in A090845.

Examples

			G.f.: A(x) = 1 + 3*x + 9*x^2 + 22*x^3 + 51*x^4 + 114*x^5 + 230*x^6 +...
Let G(x) = A(x)^(1/3)  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, A090846, A222082.

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)^3)[n+1]}
for(n=0, 60, print1(a(n), ", "))