A035840 Coordination sequence for A_14 lattice.

1, 210, 11130, 269570, 3838590, 37060506, 265953170, 1511679210, 7125357540, 28818500830, 102644594262, 328512273390, 959882556570, 2593322651430, 6545498596110, 15564971674518, 35117045235720, 75613799423610, 156153427053890, 310601807143530

Offset: 0

Author

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

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• 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 (14, -91, 364, -1001, 2002, -3003, 3432, -3003, 2002, -1001, 364, -91, 14, -1).

Programs

Mathematica

CoefficientList[Series[(x^14 + 196 x^13 + 8281 x^12 + 132496 x^11 + 1002001 x^10 + 4008004 x^9 + 9018009 x^8 + 11778624 x^7 + 9018009 x^6 + 4008004 x^5 + 1002001 x^4 + 132496 x^3 + 8281 x^2 + 196 x + 1)/(x - 1)^14, {x, 0, 30}], x] (* Vincenzo Librandi, Oct 21 2013 *)

Formula

Sum_{d=1..14} C(15, d)*C(m/2-1, d-1)*C(14-d+m/2, m/2), where norm m is always even.

G.f.: (x^14 + 196*x^13 + 8281*x^12 + 132496*x^11 + 1002001*x^10 + 4008004*x^9 + 9018009*x^8 + 11778624*x^7 + 9018009*x^6 + 4008004*x^5 + 1002001*x^4 + 132496*x^3 + 8281*x^2 + 196*x + 1) / (x-1)^14. [Colin Barker, Nov 19 2012]

Extensions

More terms from Vincenzo Librandi, Oct 21 2013