OFFSET
0,2
COMMENTS
a(0) is not an element of the recurrence. - Georg Fischer, Jul 18 2020
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 (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).
FORMULA
Sum_{d=1..16} C(17, d)*C(m/2-1, d-1)*C(16-d+m/2, m/2), where norm m is always even.
MAPLE
A := (m, n) -> `if`(m=0, 1, (n+1)*binomial(m+n-1, m)*hypergeom([1-m, 1-n, -n], [2, -m-n+1], 1)): seq(simplify(A(m, 16)), m=0..18); # Peter Luschny, Jul 18 2020
MATHEMATICA
n:=16; Table[Sum[Binomial[n+1, k]*Binomial[m-1, k-1]*Binomial[n-k+m, m], {k, 0, n}], {m, 0, n+2}] (* Georg Fischer, Jul 18 2020 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Joan Serra-Sagrista (jserra(AT)ccd.uab.es)
EXTENSIONS
a(17)-a(18) from Georg Fischer, Jul 18 2020
STATUS
approved