A035837 Coordination sequence for A_11 lattice.

1, 132, 4422, 68772, 643632, 4197468, 20934474, 85014204, 293744154, 891454124, 2432878866, 6078578508, 14097919968, 30684132468, 63221641758, 124188986196, 233931828834, 424600608564, 745616925614, 1271112537684, 2109875558208, 3418440803052

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 (11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1).

Formula

Sum_{d=1..11} C(12, d)*C(m/2-1, d-1)*C(11-d+m/2, m/2), where norm m is always even.

G.f.: -(x+1)*(x^10 + 120*x^9 + 2905*x^8 + 24320*x^7 + 84580*x^6 + 128864*x^5 + 84580*x^4 + 24320*x^3 + 2905*x^2 + 120*x + 1) / (x-1)^11. [Colin Barker, Nov 19 2012]

Mathematica

CoefficientList[Series[-(x + 1) (x^10 + 120 x^9 + 2905 x^8 + 24320 x^7 + 84580 x^6 + 128864 x^5 + 84580 x^4 + 24320 x^3 + 2905 x^2 + 120 x + 1)/(x - 1)^11, {x, 0, 30}], x] (* Vincenzo Librandi, Oct 21 2013 *)

Crossrefs

Sequence in context: A236260 A264179 A228333 * A335857 A270411 A258493

Adjacent sequences: A035834 A035835 A035836 * A035838 A035839 A035840

Keyword

nonn,easy

Author

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

Extensions

More terms from Vincenzo Librandi, Oct 21 2013

Status

approved