A035842 Coordination sequence for A_16 lattice.

1, 272, 18632, 579632, 10501172, 127485584, 1135620536, 7907476016, 45076309166, 217815522736, 916470530808, 3429182092560, 11603837100660, 35995371261360, 103501142484360, 278406848295312, 705951252118284, 1698353774374704, 3897769097766104

Offset

0,2

Comments

a(0) is not an element of the recurrence. - Georg Fischer, Jul 18 2020

Links

Table of n, a(n) for n=0..18.

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

Sequence in context: A168372 A023907 A281691 * A000518 A230531 A283230

Adjacent sequences: A035839 A035840 A035841 * A035843 A035844 A035845

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