A035846 Coordination sequence for A_20 lattice.

1, 420, 44310, 2107140, 57671880, 1041949020, 13577591370, 135798494460, 1091481669390, 7302195414780, 41800229045610, 209294745286620, 933146517188760, 3759426449644740, 13853429338548630, 47171740235162340

Offset

0,2

Links

Table of n, a(n) for n=0..15.

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 (20, -190, 1140, -4845, 15504, -38760, 77520, -125970, 167960, -184756, 167960, -125970, 77520, -38760, 15504, -4845, 1140, -190, 20, -1).

Formula

Sum_{d=1..20} C(21, d)*C(m/2-1, d-1)*C(20-d+m/2, m/2), where norm m is always even.

Crossrefs

Sequence in context: A023911 A135340 A135380 * A223941 A360537 A046167

Adjacent sequences: A035843 A035844 A035845 * A035847 A035848 A035849

Keyword

nonn,easy

Author

Joan Serra-Sagrista (jserra(AT)ccd.uab.es)

Status

approved