%I A002899 M4840 N2068
%S A002899 1,0,12,48,540,4320,42240,403200,4038300,40958400,423550512,4434978240,
%T A002899 46982827584,502437551616,5417597053440,58831951546368,642874989479580,
%U A002899 7063600894137216,77991775777488144,864910651813116480
%N A002899 Number of n-step polygons on f.c.c. lattice.
%C A002899 a(n) = number of 2-by-n matrices with entries from {1,2,3,4}, with (1) 
               second row a (multiset) permutation of the first, and (2) no constant 
               columns. [From David Callan (callan(AT)stat.wisc.edu), Aug 25 2009]
%D A002899 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002899 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002899 C. Domb, On the theory of cooperative phenomena in crystals, Advances 
               in Phys., 9 (1960), 149-361.
%D A002899 David H. Bailey, Jonathan M. Borwein, David Broadhurst and M. L. Glasser, 
               Elliptic integral evaluations of Bessel moments, arXiv:0801.0891.
%H A002899 <a href="Sindx_Fa.html#fcc">Index entries for sequences related to f.c.c. 
               lattice</a>
%o A002899 (PARI) {a(n)=sum(k=0,n,binomial(n,k)*(-4)^(n-k)*sum(j=0,k, binomial(k,
               j)^2*binomial(2*k-2*j,k-j)*binomial(2*j,j)))} print(vector(20,n,a(n-1))) 
               - David Broadhurst (D.Broadhurst(AT)open.ac.uk), Feb 06 2008
%Y A002899 Cf. A002895.
%Y A002899 Sequence in context: A061148 A052601 A003498 this_sequence A077612 A041272 
               A022282
%Y A002899 Adjacent sequences: A002896 A002897 A002898 this_sequence A002900 A002901 
               A002902
%K A002899 nonn,walk,nice
%O A002899 0,3
%A A002899 N. J. A. Sloane (njas(AT)research.att.com).
%E A002899 More terms from David Broadhurst (D.Broadhurst(AT)open.ac.uk), Feb 06 
               2008