OFFSET
0,2
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).
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
KEYWORD
nonn,easy
AUTHOR
Joan Serra-Sagrista (jserra(AT)ccd.uab.es)
STATUS
approved