A247133 Expansion of f(-x, -x^11) in powers of x where f() is a Ramanujan theta function

1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 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, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0,1

Links

Seiichi Manyama, 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 12 sequence [ -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, ...].

G.f.: Product_{k>0} (1 - x^(12*k)) * (1 - x^(12*k - 1)) * (1 - x^(12*k - 11)).

Convolution inverse of A210964.

Example

G.f. = 1 - x - x^11 + x^14 + x^34 - x^39 - x^69 + x^76 + x^116 - x^125 + ...
G.f. = q^25 - q^49 - q^289 + q^361 + q^841 - q^961 - q^1681 + q^1849 + ...

Prog

(PARI) {a(n) = my(m = 24*n + 25); if( issquare(m, &m) && (m%12==5 || m%12==7), (-1)^((m+6) \ 12))};

Crossrefs

Cf. A210964.

Sequence in context: A016360 A016412 A256434 * A186742 A016365 A016426

Adjacent sequences: A247130 A247131 A247132 * A247134 A247135 A247136

Keyword

sign

Author

Michael Somos, Jan 10 2015

Status

approved