A035745 Coordination sequence for 50-dimensional cubic lattice.

1, 100, 5000, 166700, 4170000, 83500020, 1394447000, 19980314300, 250799764000, 2802204288900, 28222682700200, 258862555329100, 2180706863326000, 16993705726247700, 123252789641763000

Offset: 0

Author

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

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• 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 (50, -1225, 19600, -230300, 2118760, -15890700, 99884400, -536878650, 2505433700, -10272278170, 37353738800, -121399651100, 354860518600, -937845656300, 2250829575120, -4923689695575, 9847379391150, -18053528883775, 30405943383200, -47129212243960, 67327446062800, -88749815264600, 108043253365600, -121548660036300, 126410606437752, -121548660036300, 108043253365600, -88749815264600, 67327446062800, -47129212243960, 30405943383200, -18053528883775, 9847379391150, -4923689695575, 2250829575120, -937845656300, 354860518600, -121399651100, 37353738800, -10272278170, 2505433700, -536878650, 99884400, -15890700, 2118760, -230300, 19600, -1225, 50, -1).

Formula

G.f.: ((1+x)/(1-x))^50.

n*a(n) = 100*a(n-1) + (n-2)*a(n-2) for n > 1. - Seiichi Manyama, Aug 31 2018

Extensions

Recomputed by N. J. A. Sloane, Nov 25 1998