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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 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 (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 Adjacent sequences: A035836 A035837 A035838 * A035840 A035841 A035842 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 December 9 06:02 EST 2023. Contains 367685 sequences. (Running on oeis4.)