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A005926 Theta series of diamond with respect to midpoint of edge.

%I A005926 M0005 #34 May 17 2023 11:29:58
%S A005926 0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A005926 0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A005926 6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,18,0,0,0
%N A005926 Theta series of diamond with respect to midpoint of edge.
%D A005926 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005926 Andy Huchala, <a href="/A005926/b005926.txt">Table of n, a(n) for n = 0..1600</a> (first 387 terms from Herman Jamke)
%H A005926 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.
%e A005926 G.f. = 2*q^(3/16) + 6*q^(19/16) + 12*q^(35/16) + 12*q^(51/16) + 6*q^(67/16) + 18*q^(83/16) + 18*q^(99/16) + ...
%t A005926 prec = 10;
%t A005926 eta[q_, a_] := Sum[q^((i + a)^2), {i, Range[-prec, prec]}];
%t A005926 t2[q_] := eta[q, 1/2];
%t A005926 t3[q_] := eta[q, 0];
%t A005926 T = Expand[t2[q^(1/2)]*(t2[q^2]*eta[q^4, 3/8] + t3[q^2]*eta[q^4, 1/8])] // PowerExpand;
%t A005926 A = Range[prec*16 + 1];
%t A005926 Do[A[[i + 1]] = Coefficient[T, q, i/16], {i, 1, prec*16}];
%t A005926 A[[1]] = 0; A  (* _Andy Huchala_, May 17 2023 *)
%Y A005926 Cf. A045840, A217513.
%K A005926 easy,nonn
%O A005926 0,4
%A A005926 _N. J. A. Sloane_
%E A005926 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 23 2008