A035841 Coordination sequence for A_15 lattice.
1, 240, 14520, 400080, 6447660, 70006512, 561075720, 3536846160, 18363363690, 81289041680, 315029394792, 1091144804400, 3433533723900, 9946019437200, 26808012135000, 67830161708592, 162298598439330, 369504358622640, 804648531335960, 1683493452034320
Offset: 0
Links
- Colin Barker, 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 (15, -105, 455, -1365, 3003, -5005, 6435, -6435, 5005, -3003, 1365, -455, 105, -15, 1).
Programs
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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
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