A035611 Coordination sequence for lattice D*_22 (with edges defined by l_1 norm = 1).

1, 44, 968, 14212, 156816, 1388508, 10286936, 65652532, 368804128, 1854105484, 8453107432, 35333619428, 136677756336, 493244610364, 1672424817272, 5360494538388, 16327295550016, 47469373288172, 132235461020168, 354093052356164, 913949931165392, 2279318877511324, 5504063080258968, 12893712963761652

Offset

0,2

Links

Table of n, a(n) for n=0..23.

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 (22, -231, 1540, -7315, 26334, -74613, 170544, -319770, 497420, -646646, 705432, -646646, 497420, -319770, 170544, -74613, 26334, -7315, 1540, -231, 22, -1).

Formula

a(m) = add(2^k*binomial(n, k)*binomial(m-1, k-1), k=0..n)+2^n*binomial((n+2*m)/2-1, n-1); with n=22.

Maple

C := (m, n) -> `if`(m=0, 1, 2^n*binomial((n+2*m)/2-1, n-1) + 2*n*hypergeom([1-m, 1-n], [2], 2)): seq(simplify(C(m, 22)), m=0..21); # Peter Luschny, Jul 18 2020

Mathematica

n:=22; Table[Sum[2^k*Binomial[n, k]*Binomial[m-1, k-1], {k, 0, n}] + 2^n*Binomial[(n+2*m)/2-1, n-1], {m, 0, n+2}] (* Georg Fischer, Jul 18 2020 *)

Crossrefs

Sequence in context: A299466 A010960 A035717 * A161679 A162182 A162413

Adjacent sequences: A035608 A035609 A035610 * A035612 A035613 A035614

Keyword

nonn,easy

Author

N. J. A. Sloane, J. Serra-Sagrista (jserra(AT)ccd.uab.es)

Extensions

More terms from Georg Fischer, Jul 18 2020

Status

approved