%I #18 Sep 07 2023 16:26:14

%S 1,0,4232,0,2987792,0,846141848,0,128975126048,0,12312430500520,0,

%T 808072815510832,0,38851092934042552,0,1433080081936088128,0,

%U 42010353222033261768,0,1006338265202317013840,0,20147944043360020434392,35184372088832,343501353331500571867744,38034306228027392

%N Coordination sequence for diamond structure D^+_46. (Edges defined by l_1 norm = 1.)

%H Ray Chandler, <a href="/A035899/b035899.txt">Table of n, a(n) for n = 0..1000</a> (first 200 terms from Georg Fischer)

%H J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (<a href="http://neilsloane.com/doc/Me220.pdf">pdf</a>).

%H Joan Serra-Sagrista, <a href="http://dx.doi.org/10.1016/S0020-0190(00)00119-8">Enumeration of lattice points in l_1 norm</a>, Inf. Proc. Lett. 76 (1-2) (2000) 39-44.

%H <a href="/index/Rec#order_92">Index entries for linear recurrences with constant coefficients</a>, signature (0, 46, 0, -1035, 0, 15180, 0, -163185, 0, 1370754, 0, -9366819, 0, 53524680, 0, -260932815, 0, 1101716330, 0, -4076350421, 0, 13340783196, 0, -38910617655, 0, 101766230790, 0, -239877544005, 0, 511738760544, 0, -991493848554, 0, 1749695026860, 0, -2818953098830, 0, 4154246671960, 0, -5608233007146, 0, 6943526580276, 0, -7890371113950, 0, 8233430727600, 0, -7890371113950, 0, 6943526580276, 0, -5608233007146, 0, 4154246671960, 0, -2818953098830, 0, 1749695026860, 0, -991493848554, 0, 511738760544, 0, -239877544005, 0, 101766230790, 0, -38910617655, 0, 13340783196, 0, -4076350421, 0, 1101716330, 0, -260932815, 0, 53524680, 0, -9366819, 0, 1370754, 0, -163185, 0, 15180, 0, -1035, 0, 46, 0, -1).

%p f := proc(m) local k,t1; t1 := 2^(n-1)*binomial((n+2*m)/2-1,n-1); if m mod 2 = 0 then t1 := t1+add(2^k*binomial(n,k)*binomial(m-1,k-1),k=0..n); fi; t1; end; where n=46.

%K nonn

%O 0,3

%A Joan Serra-Sagrista (jserra(AT)ccd.uab.es)

%E Recomputed by _N. J. A. Sloane_, Nov 27 1998

%E Zeroes inserted by _Georg Fischer_, Jul 26 2020