%I #16 Sep 07 2023 15:41:51
%S 1,0,2312,0,892432,0,138504984,0,11614313504,0,613171117352,0,
%T 22402282117680,0,604244840324920,0,12614155679414336,8589934592,
%U 211305560531644744,5111011082240,2922614819105183312
%N Coordination sequence for diamond structure D^+_34. (Edges defined by l_1 norm = 1.)
%H Ray Chandler, <a href="/A035893/b035893.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_68">Index entries for linear recurrences with constant coefficients</a>, signature (0, 34, 0, -561, 0, 5984, 0, -46376, 0, 278256, 0, -1344904, 0, 5379616, 0, -18156204, 0, 52451256, 0, -131128140, 0, 286097760, 0, -548354040, 0, 927983760, 0, -1391975640, 0, 1855967520, 0, -2203961430, 0, 2333606220, 0, -2203961430, 0, 1855967520, 0, -1391975640, 0, 927983760, 0, -548354040, 0, 286097760, 0, -131128140, 0, 52451256, 0, -18156204, 0, 5379616, 0, -1344904, 0, 278256, 0, -46376, 0, 5984, 0, -561, 0, 34, 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=34.
%K nonn
%O 0,3
%A Joan Serra-Sagrista (jserra(AT)ccd.uab.es)
%E Recomputed by _N. J. A. Sloane_, Nov 27 1998