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

%I A028610 #20 Jul 08 2025 18:40:17
%S A028610 1,4,4,8,20,16,32,16,36,28,40,4,64,40,64,56,68,40,100,48,104,80,4,56,
%T A028610 144,68,88,104,128,72,176,88,164,8,136,112,212,96,144,128,216,88,224,
%U A028610 96,20,184,176,128,304,132,236
%N A028610 Expansion of (theta_3(z)*theta_3(11z) + theta_2(z)*theta_2(11z))^2.
%C A028610 Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H A028610 Robert Israel, <a href="/A028610/b028610.txt">Table of n, a(n) for n = 0..10000</a>
%H A028610 Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H A028610 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F A028610 Convolution square of A028609. - _Michael Somos_, Mar 22 2012
%F A028610 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
%F A028610 Convolution with A032442 is A128525. - _Michael Somos_, Apr 21 2015
%e A028610 G.f. = 1 + 4*x + 4*x^2 + 8*x^3 + 20*x^4 + 16*x^5 + 32*x^6 + 16*x^7 + ...
%p A028610 S:= series((JacobiTheta3(0,z)*JacobiTheta3(0,z^11)+JacobiTheta2(0,z)*JacobiTheta2(0,z^11))^2, z, 101):
%p A028610 seq(coeff(S,z,j),j=0..100); # _Robert Israel_, Jan 21 2018
%t A028610 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 *)
%o A028610 (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 */
%o A028610 (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 */
%Y A028610 Cf. A028609, A032442, A128525.
%K A028610 nonn,look
%O A028610 0,2
%A A028610 _N. J. A. Sloane_