OFFSET
0,2
COMMENTS
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of (f(-x) / f(-x^3))^3 in powers of x where f() is a Ramanujan theta function.
Euler transform of period 3 sequence [ -3, -3, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (48 t)) = 3^(3/2) / f(t) where q = exp(2 Pi i t).
G.f.: (Product_{k>0} (1 - x^k) / (1 - x^(3*k)))^3.
a(3*n + 2) = 0.
a(0) = 1, a(n) = -(3/n)*Sum_{k=1..n} A046913(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 28 2017
EXAMPLE
1 - 3*x + 8*x^3 - 9*x^4 + 17*x^6 - 27*x^7 + 46*x^9 - 57*x^10 + 98*x^12 + ...
1/q - 3*q^3 + 8*q^11 - 9*q^15 + 17*q^23 - 27*q^27 + 46*q^35 - 57*q^39 + ...
MATHEMATICA
QP = QPochhammer; s = (QP[q]/QP[q^3])^3 + O[q]^60; CoefficientList[s, q] (* Jean-François Alcover, Nov 25 2015 *)
PROG
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x + A) / eta(x^3 + A))^3, n))}
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Nov 08 2011
STATUS
approved