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
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).
Programs
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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 *)
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]
Extensions
More terms from Vincenzo Librandi, Oct 21 2013