A035746 Coordination sequence for C_9 lattice.

1, 162, 4482, 53154, 374274, 1854882, 7159170, 22952610, 63821826, 158611106, 360027522, 758497698, 1501390338, 2818849698, 5057616258, 8724341922, 14540038146, 23507426466, 36993091970, 56826471330, 85417838082, 125897578914, 182279185794, 259648519842

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

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 (9,-36,84,-126,126,-84,36,-9,1).

Formula

a(n) = [x^(2n)] ((1+x)/(1-x))^9.

a(n) = A008418(2*n). - Seiichi Manyama, Jun 08 2018

From Chai Wah Wu, Feb 02 2023: (Start)

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n > 9.

G.f.: -(x + 1)*(x^2 + 14*x + 1)*(x^6 + 138*x^5 + 975*x^4 + 1868*x^3 + 975*x^2 + 138*x + 1)/(x - 1)^9. (End)

Crossrefs

Cf. A008418.

Sequence in context: A221871 A245955 A128803 * A285046 A022151 A279917

Adjacent sequences: A035743 A035744 A035745 * A035747 A035748 A035749

Keyword

nonn,easy

Author

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

Extensions

Recomputed by N. J. A. Sloane, Nov 25 1998

Status

approved