A028613 Expansion of theta_3(q) * theta_3(q^12) + theta_2(q) * theta_2(q^12) in powers of q^(1/4).

1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0

Offset

0,5

Links

Table of n, a(n) for n=0..104.

Formula

a(4*n + 2) = a(4*n + 3) = a(8*n + 1) = a(16*n + 8) = a(16*n + 12) = 0. - Michael Somos, Feb 22 2015

a(8*n + 5) = 4*A112607(n-1). a(16*n) = A033716(n). a(16*n + 4) = 2*A112604(n). - Michael Somos, Feb 22 2015

Example

G.f. = 1 + 2*x^4 + 4*x^13 + 2*x^16 + 4*x^21 + 2*x^36 + 4*x^37 + 2*x^48 + ...
G.f. = 1 + 2*q + 4*q^(13/4) + 2*q^4 + 4*q^(21/4) + 2*q^9 + 4*q^(37/4) + 2*q^12 + ...

Mathematica

a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, x] EllipticTheta[ 3, 0, x^12] + EllipticTheta[ 2, 0, x] EllipticTheta[ 2, 0, x^12], {x, 0, n/4}]; (* Michael Somos, Feb 22 2015 *)

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^8 + A) * eta(x^96+A))^5 / (eta(x^4 + A) * eta(x^16 + A) * eta(x^48 + A) * eta(x^192 + A))^2 + 4*x^13 * (eta(x^16 + A) * eta(x^192 + A))^2 / (eta(x^8 + A) * eta(x^96 + A)), n))};

Crossrefs

Cf. A033716, A112604, A112607.

Sequence in context: A337196 A073346 A114099 * A318381 A341755 A245515

Adjacent sequences: A028610 A028611 A028612 * A028614 A028615 A028616

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved