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

Author

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

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A008418.

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)

Extensions

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