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

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, 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, 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

Offset: 0

Author

N. J. A. Sloane

Keywords

• easy
• nonn

Examples

			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) + ...
		

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Andy Huchala, Table of n, a(n) for n = 0..1600 (first 387 terms from Herman Jamke)
• N. J. A. Sloane, Theta series and magic numbers for diamond and certain ionic crystal structures, J. Math. Phys. 28 (1987), 1653-1657.

Crossrefs

Cf. A045840, A217513.

Programs

Mathematica

prec = 10;
eta[q_, a_] := Sum[q^((i + a)^2), {i, Range[-prec, prec]}];
t2[q_] := eta[q, 1/2];
t3[q_] := eta[q, 0];
T = Expand[t2[q^(1/2)]*(t2[q^2]*eta[q^4, 3/8] + t3[q^2]*eta[q^4, 1/8])] // PowerExpand;
A = Range[prec*16 + 1];
Do[A[[i + 1]] = Coefficient[T, q, i/16], {i, 1, prec*16}];
A[[1]] = 0; A  (* Andy Huchala, May 17 2023 *)

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 23 2008