login
Theta series of f.c.c. lattice with respect to edge.
(Formerly M0940)
4

%I M0940 #25 Dec 01 2017 03:03:51

%S 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,

%T 16,12,20,24,8,28,16,8,32,20,16,16,18,20,24,24,16,24,24,8,40,20,12,40,

%U 16,12,20,24,16,40,36,16,22,24,24,32,16,12,40,32,24,28,16,24,40,28,12

%N Theta series of f.c.c. lattice with respect to edge.

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

%H G. C. Greubel, <a href="/A005884/b005884.txt">Table of n, a(n) for n = 0..1000</a>

%H N. J. A. Sloane and B. K. Teo, <a href="http://dx.doi.org/10.1063/1.449551">Theta series and magic numbers for close-packed spherical clusters</a>, J. Chem. Phys. 83 (1985) 6520-6534.

%H <a href="/index/Fa#fcc">Index entries for sequences related to f.c.c. lattice</a>

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

%t 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 *)

%o (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) ; ) ; }

%o A005884(n)={ 2*A045828(n) ; }

%o { for(n=0,100, print1(A005884(n),", ") ; ) ; } \\ _R. J. Mathar_, Jun 06 2007

%Y Cf. A045828.

%K nonn

%O 0,1

%A _N. J. A. Sloane_

%E More terms from _R. J. Mathar_, Jun 06 2007