A035868 Coordination sequence for A_42 lattice.

1, 1806, 816312, 164532018, 18756445974, 1378914676482, 71082376011528, 2723637332300766, 80988226799441304, 1932071264207861042, 37971330014459062872, 628214795343835069230, 8908241443491168857610

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 (42, -861, 11480, -111930, 850668, -5245786, 26978328, -118030185, 445891810, -1471442973, 4280561376, -11058116888, 25518731280, -52860229080, 98672427616, -166509721602, 254661927156, -353697121050, 446775310800, -513791607420, 538257874440, -513791607420, 446775310800, -353697121050, 254661927156, -166509721602, 98672427616, -52860229080, 25518731280, -11058116888, 4280561376, -1471442973, 445891810, -118030185, 26978328, -5245786, 850668, -111930, 11480, -861, 42, -1).

Formula

Sum_{d=1..42} C(43, d)*C(m/2-1, d-1)*C(42-d+m/2, m/2), where norm m is always even.

Crossrefs

Sequence in context: A252029 A250385 A345765 * A122477 A134155 A252808

Adjacent sequences: A035865 A035866 A035867 * A035869 A035870 A035871

Keyword

nonn,easy

Author

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

Status

approved