A028610 Expansion of (theta_3(z)*theta_3(11z) + theta_2(z)*theta_2(11z))^2.

1, 4, 4, 8, 20, 16, 32, 16, 36, 28, 40, 4, 64, 40, 64, 56, 68, 40, 100, 48, 104, 80, 4, 56, 144, 68, 88, 104, 128, 72, 176, 88, 164, 8, 136, 112, 212, 96, 144, 128, 216, 88, 224, 96, 20, 184, 176, 128, 304, 132, 236

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• look

Comments

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

Examples

			G.f. = 1 + 4*x + 4*x^2 + 8*x^3 + 20*x^4 + 16*x^5 + 32*x^6 + 16*x^7 + ...
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• Michael Somos, Introduction to Ramanujan theta functions
• Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Crossrefs

Cf. A028609, A032442, A128525.

Programs

Magma

A := Basis( ModularForms( Gamma1(11), 2), 51); A[1] + 4*A[2] + 4*A[3] + 8*A[4] + 20*A[5] + 16*A[6] + 32*A[7] + 16*A[8] + 36*A[9] + 28*A[10]; /* Michael Somos, Apr 21 2015 */

Maple

S:= series((JacobiTheta3(0,z)*JacobiTheta3(0,z^11)+JacobiTheta2(0,z)*JacobiTheta2(0,z^11))^2, z, 101):
seq(coeff(S,z,j),j=0..100); # Robert Israel, Jan 21 2018

Mathematica

a[ n_] := SeriesCoefficient[ (EllipticTheta[ 3, 0, q] EllipticTheta[ 3, 0, q^11] + EllipticTheta[ 2, 0, q] EllipticTheta[ 2, 0, q^11])^2, {q, 0, n}]; (* Michael Somos, Apr 21 2015 *)

PARI

{a(n) = if( n<0, 0, polcoeff( (1 + 2 * x * Ser(qfrep( [ 2, 1; 1, 6], n, 1)))^2, n))}; /* Michael Somos, Apr 21 2015 */

Formula

Convolution square of A028609. - Michael Somos, Mar 22 2012

Expansion of (phi(x) * phi(x^11) = 4 * x^3 * psi(x^2) * psi(x^22))^2 in powers of x where phi(), psi() are Ramanujan theta functions. - Michael Somos, Apr 21 2015

Convolution with A032442 is A128525. - Michael Somos, Apr 21 2015