OFFSET
1,7
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..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 the period 30 sequence [0, -1, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, -1, 2, -1, 0, 0, 0, 0, 1, -1, 0, 0, 1, -1, 1, -1, 0, 0, ...]. - Corrected by Georg Fischer, Sep 19 2020
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 A131797.
G.f.: x * Product_{k>0} (1 + x^k) * (1 + x^(15*k)) * P(15, x^k) where P(n, x) is n-th cyclotomic polynomial.
a(n) = A145783(n) unless n=0. - Michael Somos, Nov 01 2008
Convolution inverse of A058618.
EXAMPLE
G.f. = q - q^3 + q^4 - q^5 + 2*q^7 - 2*q^8 - q^9 + 2*q^10 - q^12 + 2*q^13 + ...
MATHEMATICA
QP = QPochhammer; s = QP[q^2]*(QP[q^30]/(QP[q^3]*QP[q^5])) + O[q]^80; CoefficientList[s, q] (* Jean-François Alcover, Nov 24 2015 *)
PROG
(PARI) {a(n) = my(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x^2 + A) * eta(x^30 + A) / (eta(x^3 + A) * eta(x^5 + A)), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Apr 22 2004
STATUS
approved