A205808 G.f.: Sum_{n=-oo..oo} q^(9*n^2 + 2*n).

1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

S. Cooper and M. D. Hirschhorn, Results of Hurwitz type for three squares. Discrete Math. 274 (2004), no. 1-3, 9-24. See A(q).

Formula

Expansion of f(x^7, x^11) in powers of x where f(, ) is Ramanujan's general theta function. - Michael Somos, Jan 19 2017

Euler transform of a period 36 sequence. - Michael Somos, Jan 19 2017

Example

G.f. = 1 + x^7 + x^11 + x^32 + x^40 + x^75 + x^87 + x^136 + x^152 + x^215 + ...
G.f. = q + q^64 + q^100 + q^289 + q^361 + q^676 + q^784 + q^1225 + q^1369 + ...

Mathematica

a[ n_] := SeriesCoefficient[ QPochhammer[ -x^7, x^18] QPochhammer[ -x^11, x^18] QPochhammer[ x^18], {x, 0, n}]; (* Michael Somos, Jan 19 2017 *)

Prog

(PARI) {a(n) = issquare(9*n + 1)}; /* Michael Somos, Jan 19 2017 */

Crossrefs

Characteristic function of A132355.

Sequence in context: A369643 A105165 A058342 * A238897 A373975 A374110

Adjacent sequences: A205805 A205806 A205807 * A205809 A205810 A205811

Keyword

nonn

Author

N. J. A. Sloane, Jan 31 2012

Status

approved