A244560 Expansion of f(-x^1, -x^7)^2 in powers of x where f() is Ramanujan's two-variable theta function.

1, -2, 1, 0, 0, 0, 0, -2, 2, 0, 2, -2, 0, 0, 1, 0, 0, -2, 0, 0, 1, 0, 2, -2, 0, 0, 0, -2, 2, -2, 0, 0, 2, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, -2, 2, 0, 0, -2, 0, 0, 4, -2, 1, -2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 2, 0, 2, -2, 0, -2, 0

Offset

0,2

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

G.f.: f(-x, -x^7)^2 = (Sum_{k in Z} (-1)^k * x^(4*k^2 - 3*k))^2.

Convolution square of A244525.

a(9*n) = A244526(n). a(9*n + 3) = a(9*n + 6) = 0. a(49*n + 5) = a(n-1).

Example

G.f. = 1 - 2*x + x^2 - 2*x^7 + 2*x^8 + 2*x^10 - 2*x^11 + x^14 - 2*x^17 + ...
G.f. = q^9 - 2*q^17 + q^25 - 2*q^65 + 2*q^73 + 2*q^89 - 2*q^97 + q^121 + ...

Mathematica

A244560[n_] := SeriesCoefficient[(QPochhammer[q^1, q^8]* QPochhammer[q^7, q^8]*QPochhammer[q^8, q^8])^2, {q, 0, n}]; Table[A244560[n], {n, 0, 50}] (* G. C. Greubel, Jun 17 2017 *)

Prog

(PARI) {a(n) = (-1)^n * sum(k=0, n, issquare(16*k + 9) * issquare(16*(n-k) + 9))};

Crossrefs

Cf. A244525, A244256.

Sequence in context: A219479 A113448 A123863 * A331812 A368821 A250002

Adjacent sequences: A244557 A244558 A244559 * A244561 A244562 A244563

Keyword

sign

Author

Michael Somos, Jun 30 2014

Status

approved