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A035746
Coordination sequence for C_9 lattice.
6
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
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
KEYWORD
nonn,easy
AUTHOR
Joan Serra-Sagrista (jserra(AT)ccd.uab.es)
EXTENSIONS
Recomputed by N. J. A. Sloane, Nov 25 1998
STATUS
approved