A005926 Theta series of diamond with respect to midpoint of edge. (Formerly M0005)

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

0,4

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.

Example

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) + ...

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 *)

Crossrefs

Cf. A045840, A217513.

Sequence in context: A238403 A112315 A295663 * A353419 A346483 A349378

Adjacent sequences: A005923 A005924 A005925 * A005927 A005928 A005929

Keyword

easy,nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved