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Coordination sequence for diamond structure D^+_28. (Edges defined by l_1 norm = 1.)
1

%I #16 Sep 05 2023 15:51:19

%S 1,0,1568,0,410816,0,43381856,0,2485013888,0,90102925472,0,

%T 2275791199808,0,42760561395424,3758096384,627153507629824,

%U 544923975680,7450881715909408,27028229193728,73852826419374016

%N Coordination sequence for diamond structure D^+_28. (Edges defined by l_1 norm = 1.)

%H Ray Chandler, <a href="/A035890/b035890.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_56">Index entries for linear recurrences with constant coefficients</a>, signature (0, 28, 0, -378, 0, 3276, 0, -20475, 0, 98280, 0, -376740, 0, 1184040, 0, -3108105, 0, 6906900, 0, -13123110, 0, 21474180, 0, -30421755, 0, 37442160, 0, -40116600, 0, 37442160, 0, -30421755, 0, 21474180, 0, -13123110, 0, 6906900, 0, -3108105, 0, 1184040, 0, -376740, 0, 98280, 0, -20475, 0, 3276, 0, -378, 0, 28, 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=28.

%K nonn

%O 0,3

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

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