A261615 Expansion of Product_{k>=0} (1 + x^(3*k+1))^2.

1, 2, 1, 0, 2, 4, 2, 2, 5, 4, 3, 8, 10, 6, 9, 14, 11, 14, 22, 18, 17, 30, 32, 28, 41, 46, 39, 54, 68, 60, 73, 94, 85, 96, 131, 128, 130, 170, 175, 176, 229, 246, 237, 294, 330, 320, 386, 446, 430, 492, 582, 578, 642, 762, 763, 818, 977, 1008, 1061, 1254, 1311

Offset

0,2

Comments

Self-convolution of A261612.

In general, if a > 0, b > 0, GCD(a,b) = 1 and g.f. = Product_{k>=0} (1 + x^(a*k+b))^2, then a(n) ~ exp(Pi*sqrt(2*n/(3*a))) / (2^(2*b/a + 1/4) * 3^(1/4) * a^(1/4) * n^(3/4)).

Links

Table of n, a(n) for n=0..60.

Formula

a(n) ~ exp(Pi*sqrt(2*n)/3) / (2^(11/12) * sqrt(3) * n^(3/4)).

Mathematica

nmax = 60; CoefficientList[Series[Product[(1 + x^(3*k+1))^2, {k, 0, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A022567, A035382, A261610, A261612, A261616.

Sequence in context: A108354 A329099 A329686 * A146162 A147702 A118208

Adjacent sequences: A261612 A261613 A261614 * A261616 A261617 A261618

Keyword

nonn

Author

Vaclav Kotesovec, Aug 26 2015

Status

approved