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 A217221 #22 Feb 16 2025 08:33:18
%S A217221 0,6,0,6,0,0,0,12,0,6,0,0,0,12,0,0,0,0,0,12,0,12,0,0,0,6,0,6,0,0,0,12,
%T A217221 0,0,0,0,0,12,0,12,0,0,0,12,0,0,0,0,0,18,0,0,0,0,0,0,0,12,0,0,0,12,0,
%U A217221 12,0,0,0,12,0,0,0,0,0,12,0,6,0,0,0,12,0,6,0,0,0,0,0,0,0,0,0,24,0,12,0,0,0,12,0,0,0,0,0
%N A217221 Theta series of Kagome net with respect to a deep hole.
%C A217221 Cubic AGM theta functions: a(q) (see A004016), b(q) (A005928), c(q) (A005882).
%C A217221 Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%D A217221 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag.
%H A217221 Antti Karttunen, <a href="/A217221/b217221.txt">Table of n, a(n) for n = 0..65537</a>
%H A217221 N. J. A. Sloane, <a href="http://dx.doi.org/10.1063/1.527472">Theta series and magic numbers for diamond and certain ionic crystal structures</a>, J. Math. Phys. 28 (1987), 1653-1657.
%H A217221 Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H A217221 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F A217221 Phi_0(q)-phi_0(q^4) in the notation of SPLAG, Chapter 4.
%F A217221 Expansion of a(q) - a(q^4) in powers of q where a() is a cubic AGM function. - _Michael Somos_, Feb 01 2017
%F A217221 Expansion of 6 * q * psi(q^2) * psi(q^6) in powers of q where phi(), psi() are Ramanujan theta functions. - _Michael Somos_, Feb 01 2017
%F A217221 Expansion of 6 * (eta(q^4) * eta(q^12))^2 / (eta(q^2) * eta(q^6)) in powers of q. - _Michael Somos_, Feb 01 2017
%F A217221 G.f. is a period 1 Fourier series which satisfies f(-1 / (12 t)) = 27^(1/2) (t/i) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A115978. - _Michael Somos_, Feb 01 2017
%F A217221 a(2*n) = 0. a(2*n + 1) = 6 * A033762(n). - _Michael Somos_, Feb 01 2017
%e A217221 G.f. = 6*q + 6*q^3 + 12*q^7 + 6*q^9 + 12*q^13 + 12*q^19 + 12*q^21 + ...
%t A217221 a[ n_] := If[ n < 1 || EvenQ[n], 0, 6 DivisorSum[n, Mod[(3 - #)/2, 3, -1] &]]; (* _Michael Somos_, Feb 01 2017 *)
%o A217221 (PARI) {a(n) = if( n<1 || n%2==0, 0, 6 * sumdiv(n, d, kronecker(-3, d)))}; /* _Michael Somos_, Feb 01 2017 */
%o A217221 (Magma) A := Basis( ModularForms( Gamma1(12), 1), 80); 6*A[2] + 6*A[4]; /* _Michael Somos_, Feb 01 2017 */
%Y A217221 Cf. A033762, A115978, A217220.
%K A217221 nonn
%O A217221 0,2
%A A217221 _N. J. A. Sloane_, Oct 05 2012