OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
FORMULA
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = u^2 - v + 2*v^2 - 2*u*v^2.
G.f. A(x) satisfies A(x) + A(-x) = 2*A(x^2)^2, (1 - A(x)) * (1 - A(-x)) = 1 - A(x^2).
Euler transform of period 30 sequence [ 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 2, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (30 t)) = (1/2) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A058618.
Convolution inverse of A131797.
a(n) ~ exp(2*Pi*sqrt(2*n/15)) / (2^(7/4) * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Nov 08 2015
EXAMPLE
G.f. = 1 + q + 2*q^2 + 3*q^3 + 5*q^4 + 7*q^5 + 10*q^6 + 14*q^7 + 20*q^8 + ...
MATHEMATICA
nmax = 60; CoefficientList[Series[Product[(1-x^(6*k)) * (1-x^(10*k)) / ((1-x^k) * (1-x^(15*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 08 2015 *)
QP = QPochhammer; s = QP[q^6]*(QP[q^10]/(QP[q]*QP[q^15])) + O[q]^60; CoefficientList[s, q] (* Jean-François Alcover, Nov 24 2015 *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^6 + A) * eta(x^10 + A) / eta(x + A) / eta(x^15 + A), n))};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Apr 22 2004
STATUS
approved