A035873 Coordination sequence for A_47 lattice.

1, 2256, 1273512, 320358768, 45530671524, 4166851728720, 266889766546776, 12677861331177072, 466157461593674118, 13712323126346807664, 331265632419645857880, 6714691694623273847376, 116251203402270649201092

Offset

0,2

Links

Table of n, a(n) for n=0..12.

R. Bacher, P. de la Harpe and B. Venkov, Séries de croissance et séries d'Ehrhart associées aux réseaux de racines, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142.

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 (47, -1081, 16215, -178365, 1533939, -10737573, 62891499, -314457495, 1362649145, -5178066751, 17417133617, -52251400851, 140676848445, -341643774795, 751616304549, -1503232609098, 2741188875414, -4568648125690, 6973199770790, -9762479679106, 12551759587422, -14833897694226, 16123801841550, -16123801841550, 14833897694226, -12551759587422, 9762479679106, -6973199770790, 4568648125690, -2741188875414, 1503232609098, -751616304549, 341643774795, -140676848445, 52251400851, -17417133617, 5178066751, -1362649145, 314457495, -62891499, 10737573, -1533939, 178365, -16215, 1081, -47, 1).

Formula

Sum_{d=1..47} C(48, d)*C(m/2-1, d-1)*C(47-d+m/2, m/2), where norm m is always even.

Crossrefs

Sequence in context: A077455 A068754 A222951 * A257825 A251678 A231245

Adjacent sequences: A035870 A035871 A035872 * A035874 A035875 A035876

Keyword

nonn,easy

Author

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

Status

approved