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A035838
Coordination sequence for A_12 lattice.
2
1, 156, 6162, 112268, 1219374, 9129276, 51697802, 235895244, 907129236, 3037849828, 9079799742, 24680519604, 61908797418, 144977296932, 319917948246, 670283877588, 1341750437352, 2579499722124, 4783532975546, 8588601364668, 14977318285254, 25437258929836
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 (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).
FORMULA
Sum_{d=1..12} C(13, d)*C(m/2 - 1, d - 1)*C(12 - d + m/2, m/2), where norm m is always even.
G.f.: (x^12 + 144*x^11 + 4356*x^10 + 48400*x^9 + 245025*x^8 + 627264*x^7 + 853776*x^6 + 627264*x^5 + 245025*x^4 + 48400*x^3 + 4356*x^2 + 144*x + 1) / (x - 1)^12. [Colin Barker, Nov 19 2012]
MATHEMATICA
CoefficientList[Series[(x^12 + 144 x^11 + 4356 x^10 + 48400 x^9 + 245025 x^8 + 627264 x^7 + 853776 x^6 + 627264 x^5 + 245025 x^4 + 48400 x^3 + 4356 x^2 + 144 x + 1)/(x - 1)^12, {x, 0, 30}], x] (* Vincenzo Librandi, Oct 21 2013 *)
CROSSREFS
Sequence in context: A275766 A023903 A240005 * A035824 A252778 A006112
KEYWORD
nonn,easy
AUTHOR
Joan Serra-Sagrista (jserra(AT)ccd.uab.es)
EXTENSIONS
More terms from Vincenzo Librandi, Oct 21 2013
STATUS
approved