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A035841
Coordination sequence for A_15 lattice.
2
1, 240, 14520, 400080, 6447660, 70006512, 561075720, 3536846160, 18363363690, 81289041680, 315029394792, 1091144804400, 3433533723900, 9946019437200, 26808012135000, 67830161708592, 162298598439330, 369504358622640, 804648531335960, 1683493452034320
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 (15, -105, 455, -1365, 3003, -5005, 6435, -6435, 5005, -3003, 1365, -455, 105, -15, 1).
FORMULA
Sum_{d=1..15} C(16, d)*C(m/2-1, d-1)*C(15-d+m/2, m/2), where norm m is always even.
G.f.: -(x+1)*(x^14 + 224*x^13 + 10801*x^12 + 196224*x^11 + 1667001*x^10 + 7351008*x^9 + 17699017*x^8 + 23710208*x^7 + 17699017*x^6 + 7351008*x^5 + 1667001*x^4 + 196224*x^3 + 10801*x^2 + 224*x + 1) / (x-1)^15. - Colin Barker, Mar 03 2015
PROG
(PARI) Vec(-(x +1)*(x^14 +224*x^13 +10801*x^12 +196224*x^11 +1667001*x^10 +7351008*x^9 +17699017*x^8 +23710208*x^7 +17699017*x^6 +7351008*x^5 +1667001*x^4 +196224*x^3 +10801*x^2 +224*x +1) / (x -1)^15 + O(x^100)) \\ Colin Barker, Mar 03 2015
CROSSREFS
Sequence in context: A023906 A292883 A292075 * A232428 A338562 A342990
KEYWORD
nonn,easy
AUTHOR
Joan Serra-Sagrista (jserra(AT)ccd.uab.es)
STATUS
approved