A192323 Expansion of theta_3(q^3) * theta_3(q^5) in powers of q.

1, 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 6, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 6, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0,4

Links

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

Formula

Expansion of (eta(q^6) * eta(q^10))^5 / (eta(q^3) * eta(q^5) * eta(q^12) * eta(q^20))^2 in powers of q.

Euler transform of a period 60 sequence.

G.f.: (Sum_{k} x^(3 * k^2)) * (Sum_{k} x^(5 * k^2)).

a(3*n + 1) = a(4*n + 2) = a(5*n + 1) = a(5*n + 4) = 0. a(4*n) = A028956(n).

a(n) = A122855(n) - A140727(n). a(5*n) = A260671(n).

Example

G.f. = 1 + 2*q^3 + 2*q^5 + 4*q^8 + 2*q^12 + 4*q^17 + 2*q^20 + 4*q^23 + 2*q^27 + ...

Mathematica

a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q^3] EllipticTheta[ 3, 0, q^5], {q, 0, n}];

Prog

(PARI) {a(n) = if( n<1, n==0, qfrep([3, 0; 0, 5], n)[n]*2)};
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^6 + A) * eta(x^10 + A))^5 / (eta(x^3 + A) * eta(x^5 + A) * eta(x^12 + A) * eta(x^20 + A))^2, n))};

Crossrefs

Cf. A028956, A122855, A140727, A260671.

Sequence in context: A298100 A303636 A073274 * A242848 A071957 A329186

Adjacent sequences: A192320 A192321 A192322 * A192324 A192325 A192326

Keyword

nonn

Author

Michael Somos, Aug 01 2011

Status

approved