A035871 Coordination sequence for A_45 lattice.

1, 2070, 1072260, 247572690, 32307967980, 2716364821590, 159949347063420, 6990685556924610, 236719501733097990, 6419344706383457730, 143128273365369593820, 2680836476183238990870, 42942924344438274913260

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 (45, -990, 14190, -148995, 1221759, -8145060, 45379620, -215553195, 886163135, -3190187286, 10150595910, -28760021745, 73006209045, -166871334960, 344867425584, -646626422970, 1103068603890, -1715884494940, 2438362177020, -3169870830126, 3773655750150, -4116715363800, 4116715363800, -3773655750150, 3169870830126, -2438362177020, 1715884494940, -1103068603890, 646626422970, -344867425584, 166871334960, -73006209045, 28760021745, -10150595910, 3190187286, -886163135, 215553195, -45379620, 8145060, -1221759, 148995, -14190, 990, -45, 1).

Formula

Sum_{d=1..45} C(46, d)*C(m/2-1, d-1)*C(45-d+m/2, m/2), where norm m is always even.

Crossrefs

Sequence in context: A065217 A249288 A200829 * A221052 A062913 A096927

Adjacent sequences: A035868 A035869 A035870 * A035872 A035873 A035874

Keyword

nonn,easy

Author

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

Status

approved