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

0,2

Comments

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

Links

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

Example

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.

Prog

(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), ", "))

Crossrefs

Cf. A090845, A090846, A222082.

Sequence in context: A000716 A001628 A099166 * A305612 A202882 A350105

Adjacent sequences: A222080 A222081 A222082 * A222084 A222085 A222086

Keyword

nonn

Author

Paul D. Hanna, Feb 06 2013

Status

approved