A005886 Theta series of f.c.c. lattice with respect to tetrahedral hole.

4, 12, 12, 16, 24, 12, 24, 36, 12, 28, 36, 24, 36, 36, 24, 24, 60, 36, 28, 48, 12, 60, 60, 24, 48, 48, 36, 48, 60, 24, 52, 84, 48, 24, 60, 36, 48, 96, 36, 72, 48, 36, 72, 60, 48, 52, 96, 36, 60, 96, 24, 72, 108, 24, 48, 60, 72, 96, 84, 60, 48, 108, 36, 52, 72, 60, 108, 108, 36, 48, 108

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Empirically, the number of integral quadruples with sum = 1, sum-of-squares = 2n-1. - Colin Mallows, Dec 31 2016

Examples

			4 + 12*x + 12*x^2 + 16*x^3 + 24*x^4 + 12*x^5 + 24*x^6 + 36*x^7 + 12*x^8 + ...
		

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
• G. Nebe and N. J. A. Sloane, Home page for this lattice
• 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 f.c.c. lattice

Crossrefs

Cf. A005869, A005878, A008443. Partial sums is A121054. Cf also A278081-A278086.

Programs

Mathematica

QP = QPochhammer; CoefficientList[4(QP[q^2]^2/QP[q])^3 + O[q]^50, q] (* Jean-François Alcover, Jul 04 2017, after Michael Somos *)

Formula

a(n) = 1/2 * A005878(n) = 2 * A005869(n) = 4 * A008443(n). - Michael Somos, May 31 2012

Extensions

Terms a(50) onward added by G. C. Greubel, Feb 20 2018