A005869 Theta series of b.c.c. lattice with respect to short edge. (Formerly M1561)

2, 6, 6, 8, 12, 6, 12, 18, 6, 14, 18, 12, 18, 18, 12, 12, 30, 18, 14, 24, 6, 30, 30, 12, 24, 24, 18, 24, 30, 12, 26, 42, 24, 12, 30, 18, 24, 48, 18, 36, 24, 18, 36, 30, 24, 26, 48, 18, 30, 48, 12, 36, 54, 12, 24, 30, 36, 48, 42, 30, 24, 54, 18, 26, 36, 30, 54, 54, 18, 24

Offset

0,1

References

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

N. J. A. Sloane and B. K. Teo, Theta series and magic numbers for close-packed spherical clusters, J. Chem. Phys. 83 (1985) 6520-6534.

Index entries for sequences related to b.c.c. lattice

Formula

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = (1/2) * exp(3*Pi/8) * Pi^(3/4) * 2^(1/8) / Gamma(3/4)^3 = A388165. - Simon Plouffe, Sep 15 2025

Mathematica

QP = QPochhammer; CoefficientList[2*(QP[q^2]^2/QP[q])^3 + O[q]^70, q] (* Jean-François Alcover, Jul 05 2017, after Michael Somos *)

Crossrefs

Cf. A008443. Equals A005886/2. Cf. A121055.

Sequence in context: A157299 A230292 A082911 * A353624 A391780 A377998

Adjacent sequences: A005866 A005867 A005868 * A005870 A005871 A005872

Keyword

nonn

Author

N. J. A. Sloane

Status

approved