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Coordination sequence for diamond structure D^+_36. (Edges defined by l_1 norm = 1.)
1

%I #17 Sep 07 2023 15:43:38

%S 1,0,2592,0,1121472,0,194986080,0,18300435840,0,1080041397408,0,

%T 44042615547456,0,1323529602867936,0,30721376739859200,0,

%U 570951082378155808,1236950581248,8740628929823039424

%N Coordination sequence for diamond structure D^+_36. (Edges defined by l_1 norm = 1.)

%H Ray Chandler, <a href="/A035894/b035894.txt">Table of n, a(n) for n = 0..1000</a>

%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_72">Index entries for linear recurrences with constant coefficients</a>, signature (0, 36, 0, -630, 0, 7140, 0, -58905, 0, 376992, 0, -1947792, 0, 8347680, 0, -30260340, 0, 94143280, 0, -254186856, 0, 600805296, 0, -1251677700, 0, 2310789600, 0, -3796297200, 0, 5567902560, 0, -7307872110, 0, 8597496600, 0, -9075135300, 0, 8597496600, 0, -7307872110, 0, 5567902560, 0, -3796297200, 0, 2310789600, 0, -1251677700, 0, 600805296, 0, -254186856, 0, 94143280, 0, -30260340, 0, 8347680, 0, -1947792, 0, 376992, 0, -58905, 0, 7140, 0, -630, 0, 36, 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=36.

%K nonn

%O 0,3

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

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