This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A033765 #24 Feb 16 2025 08:32:36
%S A033765 1,1,1,3,1,2,5,2,3,7,4,4,10,3,3,11,6,4,12,6,5,19,6,8,16,7,10,17,7,8,
%T A033765 25,10,9,20,8,8,27,12,11,30,11,14,27,12,14,29,14,12,37,15,11,42,15,14,
%U A033765 34,12,16,44,18,16,36,18,17,39,17,20,59,18,19,42,22,24,49
%N A033765 Product t2(q^d); d | 6, where t2 = theta2(q)/(2*q^(1/4)).
%C A033765 Quadratic AGM theta functions: a(q) (see A004018), b(q) (A104794), c(q) (A005883).
%C A033765 Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%C A033765 Also the number of positive odd solutions to equation a^2 + 2*b^2 + 3*c^2 + 6*d^2 = 8*n + 12. - _Seiichi Manyama_, May 29 2017
%H A033765 Seiichi Manyama, <a href="/A033765/b033765.txt">Table of n, a(n) for n = 0..10000</a>
%H A033765 Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H A033765 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F A033765 Expansion of q^(-3) * (a(q) - a(q^3)) * c(q) / 16 in powers of q^2 where a(), c() are quadratic AGM theta functions. - _Michael Somos_, Sep 30 2013
%F A033765 Expansion of (phi(x)^2 - phi(x^3)^2) * psi(x^2)^2 / 4 in powers of x where phi(), psi() are Ramanujan theta functions. - _Michael Somos_, Sep 30 2013
%e A033765 G.f. = 1 + x + x^2 + 3*x^3 + x^4 + 2*x^5 + 5*x^6 + 2*x^7 + 3*x^8 + 7*x^9 + ...
%e A033765 G.f. = q^3 + q^5 + q^7 + 3*q^9 + q^11 + 2*q^13 + 5*q^15 + 2*q^17 + 3*q^19 + ...
%t A033765 a[ n_] := SeriesCoefficient[ EllipticTheta[ 2, 0, q] EllipticTheta[ 2, 0, q^2] EllipticTheta[ 2, 0, q^3] EllipticTheta[ 2, 0, q^6] / 16, {q, 0, 2 n + 3}]; (* _Michael Somos_, Sep 30 2013 *)
%o A033765 (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A) * eta(x^4 + A)^2 * eta(x^6 + A) * eta(x^12 + A)^2 / (eta(x + A) * eta(x^3 + A)), n))}; /* _Michael Somos_, Sep 30 2013 */
%o A033765 (Magma) A := Basis( ModularForms( Gamma0(24), 2), 105); A[4] + A[6]; /* _Michael Somos_, Aug 24 2014 */
%K A033765 nonn
%O A033765 0,4
%A A033765 _N. J. A. Sloane_
%E A033765 More terms from _Seiichi Manyama_, May 22 2017