login
A035837
Coordination sequence for A_11 lattice.
2
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
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
KEYWORD
nonn,easy
AUTHOR
Joan Serra-Sagrista (jserra(AT)ccd.uab.es)
EXTENSIONS
More terms from Vincenzo Librandi, Oct 21 2013
STATUS
approved