A035885 - OEIS

%I #22 Sep 05 2023 15:47:48

%S 1,0,648,0,70416,0,3116952,0,76117536,131072,1205253288,22413312,

%T 13740702000,784465920,121013567928,13231325184,863382367296,

%U 141764198400,5162116908744,1105760747520,26542312890192,6802103992320,119826539041752,34758003916800,483178115916384

%N Coordination sequence for diamond structure D^+_18. (Edges defined by l_1 norm = 1.)

%H Ray Chandler, <a href="/A035885/b035885.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_36">Index entries for linear recurrences with constant coefficients</a>, signature (0, 18, 0, -153, 0, 816, 0, -3060, 0, 8568, 0, -18564, 0, 31824, 0, -43758, 0, 48620, 0, -43758, 0, 31824, 0, -18564, 0, 8568, 0, -3060, 0, 816, 0, -153, 0, 18, 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=18.

%t f[m_] := Module[{n = 18, t1}, t1 = 2^(n-1)*Binomial[(n+2m)/2 - 1, n-1]; If[EvenQ[m], t1 = t1 + Sum[2^k*Binomial[n, k]* Binomial[m-1, k-1], {k, 0, n}]]; t1];

%t Table[f[m], {m, 0, 24}] (* _Jean-François Alcover_, Mar 23 2023, after Maple code *)

%K nonn

%O 0,3

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

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