A005884 Theta series of f.c.c. lattice with respect to edge. (Formerly M0940)

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

0,1

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 f.c.c. lattice

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A045828.

Sequence in context: A107748 A338506 A353190 * A229913 A285326 A355467

Adjacent sequences: A005881 A005882 A005883 * A005885 A005886 A005887

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved