A035748 Coordination sequence for C_11 lattice.

1, 242, 9922, 170610, 1690370, 11414898, 58227906, 240089586, 838478850, 2564399090, 7039035586, 17664712562, 41110086402, 89719625842, 185263467202, 364571790066, 687750033410, 1249849661170, 2197075886786, 3748850875506, 6227320558338, 10096197409650

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

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.

Formula

a(n) = [x^(2n)] ((1+x)/(1-x))^11.

From Robert Israel, Sep 07 2018: (Start)

G.f.: cosh(22*arctanh(sqrt(x))).

(-2*n^2-n)*a(n)+(4*n^2+8*n+246)*a(n+1)+(-2*n^2-7*n-6)*a(n+2)=0. (End)

Maple

f:= gfun:-rectoproc({(-2*n^2-n)*a(n)+(4*n^2+8*n+246)*a(n+1)+(-2*n^2-7*n-6)*a(n+2), a(0)=1, a(1)=242}, a(n), remember):
seq(f(n), n=0..100);

Mathematica

RecurrenceTable[{(4*n^2 + 8*n + 246)*a[n+1] + (-2*n^2 - 7*n - 6)*a[n+2] + (-2*n^2 - n)*a[n] == 0, a[0] == 1, a[1] == 242}, a, {n, 0, 100}] (* Jean-François Alcover, Sep 16 2022, after Maple program *)

Crossrefs

Sequence in context: A318529 A006601 A283723 * A022153 A335611 A194788

Adjacent sequences: A035745 A035746 A035747 * A035749 A035750 A035751

Keyword

nonn,easy

Author

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

Extensions

Recomputed by N. J. A. Sloane, Nov 25 1998

Status

approved