The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A028610 Expansion of (theta_3(z)*theta_3(11z) + theta_2(z)*theta_2(11z))^2. 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). 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 Convolution with A032442 is A128525. - 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 Cf. A028609, A032442, A128525. Sequence in context: A261212 A112435 A232508 * A019171 A038551 A004049 Adjacent sequences: A028607 A028608 A028609 * A028611 A028612 A028613 KEYWORD nonn,look AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 28 18:51 EST 2022. Contains 358421 sequences. (Running on oeis4.)