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Coordination sequence for diamond structure D^+_26. (Edges defined by l_1 norm = 1.)
1

%I #16 Sep 05 2023 15:50:47

%S 1,0,1352,0,305552,0,27866072,0,1381251872,0,43450388072,0,

%T 955155127472,33554432,15676941638904,11777605632,201710366471744,

%U 796951314432,2112804738688904,24705490747392,18563618015178704

%N Coordination sequence for diamond structure D^+_26. (Edges defined by l_1 norm = 1.)

%H Ray Chandler, <a href="/A035889/b035889.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_52">Index entries for linear recurrences with constant coefficients</a>, signature (0, 26, 0, -325, 0, 2600, 0, -14950, 0, 65780, 0, -230230, 0, 657800, 0, -1562275, 0, 3124550, 0, -5311735, 0, 7726160, 0, -9657700, 0, 10400600, 0, -9657700, 0, 7726160, 0, -5311735, 0, 3124550, 0, -1562275, 0, 657800, 0, -230230, 0, 65780, 0, -14950, 0, 2600, 0, -325, 0, 26, 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=26.

%K nonn

%O 0,3

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

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