OFFSET
3,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 3..1000
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Euler transform of period 9 sequence [ -3, 0, 1, 3, 3, 1, 0, -3, -2, ...].
EXAMPLE
G.f. = q^3 - 3*q^4 + 3*q^5 - 3*q^8 + q^9 + 3*q^10 - 2*q^12 - 3*q^13 + ...
MATHEMATICA
a[ n_] := If[ n < 3, 0, With[{m = n - 3}, SeriesCoefficient[ q^3 Product[ (1 - q^k)^{3, 0, -1, -3, -3, -1, 0, 3, 2}[[Mod[k, 9, 1]]], {k, m}], {q, 0, n}]]];
PROG
(PARI) {a(n) = if( n<3, 0, n-=3; polcoeff( prod(k=1, n, (1 - x^k + x * O(x^n))^[2, 3, 0, -1, -3, -3, -1, 0, 3][k%9 + 1]), n))};
(Magma) Basis( ModularForms( Gamma1(9), 1), 82) [4];
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, May 06 2015
STATUS
approved