OFFSET
0,11
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Euler transform of period 16 sequence [ 1, -2, 0, -1, 0, -1, 1, -2, 1, -1, 0, -1, 0, -2, 1, -2, ...].
G.f.: (Sum_{k} (-1)^k * x^(3*k^2 + k)) * (Sum_{k} x^(4*k^2 + 3*k)).
a(n) = - A143379(2*n+1).
EXAMPLE
1 + x - x^2 - x^3 - x^4 - x^5 + x^7 - x^9 + 2*x^10 - x^12 + x^15 + x^17 + ...
q^31 + q^79 - q^127 - q^175 - q^223 - q^271 + q^367 - q^463 + 2*q^511 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ q^2] QPochhammer[ q^8] QPochhammer[ -q^1, q^8] QPochhammer[ -q^7, q^8], {q, 0, n}]
PROG
(PARI) {a(n) = local(s, v); if( n<0, 0, n = 48*n + 31; forstep( u=1, sqrtint( n\4), 2, if( u%3 && issquare( (n - 4*u^2)/3, &v), s += (-1)^((u+1)\6))); s)}
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Jul 11 2012
STATUS
approved