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

0,2

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).

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]

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 *)

Crossrefs

Sequence in context: A185042 A323963 A023905 * A140904 A092711 A187308

Adjacent sequences: A035837 A035838 A035839 * A035841 A035842 A035843

Keyword

nonn,easy

Author

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

Extensions

More terms from Vincenzo Librandi, Oct 21 2013

Status

approved