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A035901 Coordination sequence for diamond structure D^+_50. (Edges defined by l_1 norm = 1.)

%I A035901 #25 Sep 07 2023 16:36:14
%S A035901 1,0,5000,0,4170000,0,1394447000,0,250799764000,0,28222682700200,0,
%T A035901 2180706863326000,0,123252789641763000,0,5335428332027176000,0,
%U A035901 183203070393610797000,0,5129723834328569406800,0,119780004243882975543000,0,2376073555319729124284000,562949953421312,40672867115498596760897000
%N A035901 Coordination sequence for diamond structure D^+_50. (Edges defined by l_1 norm = 1.)
%C A035901 Differs from A035787 first at a(13). - _R. J. Mathar_, Mar 06 2010
%H A035901 Ray Chandler, <a href="/A035901/b035901.txt">Table of n, a(n) for n = 0..1000</a> (first 200 terms from Georg Fischer)
%H A035901 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 A035901 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 A035901 <a href="/index/Rec#order_100">Index entries for linear recurrences with constant coefficients</a>, signature (0, 50, 0, -1225, 0, 19600, 0, -230300, 0, 2118760, 0, -15890700, 0, 99884400, 0, -536878650, 0, 2505433700, 0, -10272278170, 0, 37353738800, 0, -121399651100, 0, 354860518600, 0, -937845656300, 0, 2250829575120, 0, -4923689695575, 0, 9847379391150, 0, -18053528883775, 0, 30405943383200, 0, -47129212243960, 0, 67327446062800, 0, -88749815264600, 0, 108043253365600, 0, -121548660036300, 0, 126410606437752, 0, -121548660036300, 0, 108043253365600, 0, -88749815264600, 0, 67327446062800, 0, -47129212243960, 0, 30405943383200, 0, -18053528883775, 0, 9847379391150, 0, -4923689695575, 0, 2250829575120, 0, -937845656300, 0, 354860518600, 0, -121399651100, 0, 37353738800, 0, -10272278170, 0, 2505433700, 0, -536878650, 0, 99884400, 0, -15890700, 0, 2118760, 0, -230300, 0, 19600, 0, -1225, 0, 50, 0, -1).
%p A035901 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=50.
%t A035901 n = 50;
%t A035901 f[m_] := Module[{k, 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 A035901 f /@ Range[0, 22, 2] (* _Jean-François Alcover_, Apr 07 2020, from Maple *)
%K A035901 nonn
%O A035901 0,3
%A A035901 Joan Serra-Sagrista (jserra(AT)ccd.uab.es)
%E A035901 Recomputed by _N. J. A. Sloane_, Nov 27 1998
%E A035901 Zeroes inserted by _Georg Fischer_, Jul 26 2020