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

Author

Michael Somos, Aug 01 2011

Keywords

• nonn

Examples

			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 + ...
		

Links

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

Crossrefs

Cf. A028956, A122855, A140727, A260671.

Programs

Mathematica

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

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))};

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).