OFFSET
0,4
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
f(x,x^m) = 1 + Sum_{k=1..oo} x^((m+1)*k*(k-1)/2) (x^k + x^(m*k)). - N. J. A. Sloane, Jan 30 2017
Euler transform of period 18 sequence [1, 0, 1, -2, 1, -1, 2, -1, 0, -1, 2, -1, 1, -2, 1, 0, 1, -2, ...].
G.f.: (Sum_{k>0} x^(k*(k - 1)/2)) * (Sum_{k in Z} x^(k*(9*k + 5)/2)).
G.f.: Product_{k>0} (1 - x^(2*k)) / (1 - x^(2*k-1)) * (1 + x^(9*k-7)) * (1 + x^(9*k-2)) * (1 - x^(9*k)).
2 * a(n) = A281451(8*n + 3).
EXAMPLE
G.f. = 1 + x + x^2 + 2*x^3 + x^5 + x^6 + x^7 + 2*x^8 + 2*x^10 + x^12 + ...
G.f. = q^17 + q^53 + q^89 + 2*q^125 + q^197 + q^233 + q^269 + 2*q^305 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ (1/2) x^(-1/8) EllipticTheta[ 2, 0, x^(1/2)] QPochhammer[ -x^2, x^9] QPochhammer[ -x^7, x^9] QPochhammer[ x^9], {x, 0, n}];
PROG
(PARI) {a(n) = if( n<0, 0, sumdiv(36*n + 17, d, kronecker(-4, d)) / 2)};
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Michael Somos, Jan 29 2017
STATUS
approved