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A259896 Expansion of psi(x) * psi(x^6) in powers of x where phi() is a Ramanujan theta function. 6
1, 1, 0, 1, 0, 0, 2, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 3, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 0, 1, 1, 0, 2, 1, 0, 2, 0, 0, 2, 0, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0, 1, 1, 0, 1, 0, 0, 1, 2, 0, 2, 1, 0, 2, 0, 0, 0, 1, 0, 2, 1, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

Also the number of positive odd solutions to equation x^2 + 6*y^2 = 8*n + 7. - Seiichi Manyama, May 28 2017

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(-7/8) * eta(q^2)^2 * eta(q^12)^2 / (eta(q) * eta(q^6)) in powers of q.

Euler transform of period 12 sequence [ 1, -1, 1, -1, 1, 0, 1, -1, 1, -1, 1, -2, ...].

a(3*n + 1) = A259895(n). a(3*n + 2) = a(9*n + 4) = 0.

EXAMPLE

G.f. = 1 + x + x^3 + 2*x^6 + x^7 + x^9 + x^10 + x^12 + x^15 + x^16 + ...

G.f. = q^7 + q^15 + q^31 + 2*q^55 + q^63 + q^79 + q^87 + q^103 + q^127 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ EllipticTheta[ 2, 0, x^(1/2)] EllipticTheta[ 2, 0, x^3] / (4 q^(7/8)), {x, 0, n}];

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^12 + A)^2 / (eta(x + A) * eta(x^6 + A)), n))};

CROSSREFS

Cf. A259895.

Sequence in context: A045706 A045634 A141702 * A113313 A074871 A182641

Adjacent sequences:  A259893 A259894 A259895 * A259897 A259898 A259899

KEYWORD

nonn

AUTHOR

Michael Somos, Jul 07 2015

STATUS

approved

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Last modified June 20 05:01 EDT 2019. Contains 324229 sequences. (Running on oeis4.)