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

1, 0, 5000, 0, 4170000, 0, 1394447000, 0, 250799764000, 0, 28222682700200, 0, 2180706863326000, 0, 123252789641763000, 0, 5335428332027176000, 0, 183203070393610797000, 0, 5129723834328569406800, 0, 119780004243882975543000, 0, 2376073555319729124284000, 562949953421312, 40672867115498596760897000

Offset: 0

Author

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

Keywords

• nonn

Comments

Differs from A035787 first at a(13). - R. J. Mathar, Mar 06 2010

Links

• Ray Chandler, Table of n, a(n) for n = 0..1000 (first 200 terms from Georg Fischer)
• J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
• Joan Serra-Sagrista, Enumeration of lattice points in l_1 norm, Inf. Proc. Lett. 76 (1-2) (2000) 39-44.
• Index entries for linear recurrences with constant coefficients, 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).

Programs

Maple

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.

Mathematica

n = 50;
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];
f /@ Range[0, 22, 2] (* Jean-François Alcover, Apr 07 2020, from Maple *)

Extensions

Recomputed by N. J. A. Sloane, Nov 27 1998

Zeroes inserted by Georg Fischer, Jul 26 2020