A005884 Theta series of f.c.c. lattice with respect to edge.

2, 4, 4, 8, 6, 4, 12, 8, 8, 12, 8, 8, 14, 16, 4, 16, 16, 8, 20, 8, 8, 20, 20, 16, 18, 8, 12, 24, 16, 12, 20, 24, 8, 28, 16, 8, 32, 20, 16, 16, 18, 20, 24, 24, 16, 24, 24, 8, 40, 20, 12, 40, 16, 12, 20, 24, 16, 40, 36, 16, 22, 24, 24, 32, 16, 12, 40, 32, 24, 28, 16, 24, 40, 28, 12

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

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 f.c.c. lattice

Crossrefs

Cf. A045828.

Programs

Mathematica

QP = QPochhammer; s = 2 QP[q^2]^3*QP[q^4]^2/QP[q]^2 + O[q]^75; CoefficientList[s, q] (* Jean-François Alcover, Jul 04 2017 *)

PARI

A045828(n)={ if(n<0, 0, A=x*O(x^n) ; polcoeff( eta(x^2+A)^3*eta(x^4+A)^2/eta(x+A)^2, n) ; ) ; }
A005884(n)={ 2*A045828(n) ; }
{ for(n=0,100, print1(A005884(n),", ") ; ) ; } \\ R. J. Mathar, Jun 06 2007

Formula

a(n) = 2*A045828(n).

Extensions

More terms from R. J. Mathar, Jun 06 2007