A035863 Coordination sequence for A_37 lattice.

1, 1406, 494912, 77756018, 6920161874, 398019718826, 16094610778352, 485262943621094, 11394625956532886, 215500967075111278, 3371762603125563792, 44608224481707201954, 508174845038478558618

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 (37, -666, 7770, -66045, 435897, -2324784, 10295472, -38608020, 124403620, -348330136, 854992152, -1852482996, 3562467300, -6107086800, 9364199760, -12875774670, 15905368710, -17672631900, 17672631900, -15905368710, 12875774670, -9364199760, 6107086800, -3562467300, 1852482996, -854992152, 348330136, -124403620, 38608020, -10295472, 2324784, -435897, 66045, -7770, 666, -37, 1).

Formula

Sum_{d=1..37} C(38, d)*C(m/2-1, d-1)*C(37-d+m/2, m/2), where norm m is always even.

Crossrefs

Sequence in context: A022058 A107522 A158764 * A045127 A210786 A187957

Adjacent sequences: A035860 A035861 A035862 * A035864 A035865 A035866

Keyword

nonn,easy

Author

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

Extensions

a(11) corrected, a(12) added by Ray Chandler, Jan 19 2016

Status

approved