OFFSET
0,2
COMMENTS
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
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
EXAMPLE
G.f. = 1 + 4*x + 4*x^2 + 8*x^3 + 20*x^4 + 16*x^5 + 32*x^6 + 16*x^7 + ...
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 *)
PROG
(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 */
(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 */
CROSSREFS
KEYWORD
nonn,look
AUTHOR
STATUS
approved