A005886 Theta series of f.c.c. lattice with respect to tetrahedral hole. (Formerly M3429)

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

0,1

Comments

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

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

Formula

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A074258 A253137 A120213 * A096442 A211437 A195199

Adjacent sequences: A005883 A005884 A005885 * A005887 A005888 A005889

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved