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A035842 Coordination sequence for A_16 lattice. 0
1, 272, 18632, 579632, 10501172, 127485584, 1135620536, 7907476016, 45076309166, 217815522736, 916470530808, 3429182092560, 11603837100660, 35995371261360, 103501142484360, 278406848295312, 705951252118284, 1698353774374704, 3897769097766104 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 3 14:46 EDT 2020. Contains 336198 sequences. (Running on oeis4.)