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
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.
Programs
-
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 *)
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)
Extensions
Recomputed by N. J. A. Sloane, Nov 25 1998