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A035839 Coordination sequence for A_13 lattice. 2
1, 182, 8372, 176722, 2206932, 18827718, 120353324, 614266354, 2619716554, 9654482474, 31534801116, 93093230958, 252208679268, 634756203018, 1498750896708, 3346707628446, 7114703302434, 14479567043214, 28342922553764, 53573492643034, 98118326104708 (list; graph; refs; listen; history; text; internal format)
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 (13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1).
FORMULA
Sum_{d=1..13} C(14, d)*C(m/2-1, d-1)*C(13-d+m/2, m/2), where norm m is always even.
G.f.: -(x+1)*(x^12 + 168*x^11 + 5916*x^10 + 75880*x^9 + 435345*x^8 + 1221024*x^7 + 1723632*x^6 + 1221024*x^5 + 435345*x^4 + 75880*x^3 + 5916*x^2 + 168*x + 1) / (x-1)^13. [Colin Barker, Nov 19 2012]
MATHEMATICA
CoefficientList[Series[-(x + 1) (x^12 + 168 x^11 + 5916 x^10 + 75880 x^9 + 435345 x^8 + 1221024 x^7 + 1723632 x^6 + 1221024 x^5 + 435345 x^4 + 75880 x^3 + 5916 x^2 + 168 x + 1)/(x - 1)^13, {x, 0, 30}], x] (* Vincenzo Librandi, Oct 21 2013 *)
CROSSREFS
Sequence in context: A209852 A321637 A023904 * A048546 A225712 A015306
KEYWORD
nonn,easy
AUTHOR
Joan Serra-Sagrista (jserra(AT)ccd.uab.es)
EXTENSIONS
More terms from Vincenzo Librandi, Oct 21 2013
STATUS
approved

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Last modified March 28 07:20 EDT 2024. Contains 371235 sequences. (Running on oeis4.)