A035874 Coordination sequence for A_48 lattice.

1, 2352, 1384152, 362955152, 53762385852, 5126650450992, 342037616253032, 16917775827266832, 647441209728416082, 19812657149517726032, 497675838364649446152, 10483172845268383890672, 188497102616595297692972

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 (48, -1128, 17296, -194580, 1712304, -12271512, 73629072, -377348994, 1677106640, -6540715896, 22595200368, -69668534468, 192928249296, -482320623240, 1093260079344, -2254848913647, 4244421484512, -7309837001104, 11541847896480, -16735679449896, 22314239266528, -27385657281648, 30957699535776, -32247603683100, 30957699535776, -27385657281648, 22314239266528, -16735679449896, 11541847896480, -7309837001104, 4244421484512, -2254848913647, 1093260079344, -482320623240, 192928249296, -69668534468, 22595200368, -6540715896, 1677106640, -377348994, 73629072, -12271512, 1712304, -194580, 17296, -1128, 48, -1).

Formula

Sum_{d=1..48} C(49, d)*C(m/2-1, d-1)*C(48-d+m/2, m/2), where norm m is always even.

Crossrefs

Sequence in context: A234078 A219193 A063517 * A226267 A251295 A220626

Adjacent sequences: A035871 A035872 A035873 * A035875 A035876 A035877

Keyword

nonn,easy

Author

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

Extensions

a(9) corrected, a(10)-a(12) added by Ray Chandler, Jan 19 2016

Status

approved