A022150 Coordination sequence for root lattice B_8.

1, 128, 3264, 34624, 216448, 954880, 3301952, 9556160, 24165120, 54993792, 115021760, 224533056, 413862016, 726758656, 1224437056, 1990370240, 3135895040, 4806690432, 7190192832, 10524011840, 15105409920, 21301909504, 29563091008, 40433645248, 54567743744

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

M. Baake and U. Grimm, Coordination sequences for root lattices and related graphs, arXiv:cond-mat/9706122, Zeit. f. Kristallographie, 212 (1997), 253-256.

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.

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

a(0) = 1; for n > 0, a(n) = (3968*n^7 - 6720*n^6 + 35840*n^5 - 36960*n^4 + 60032*n^3 - 26880*n^2 + 11040*n)/315. - Philippe Deléham, Feb 20 2004

G.f.: (x^8 + 568*x^7 + 5852*x^6 + 18888*x^5 + 23750*x^4 + 12040*x^3 + 2268*x^2 + 120*x +1 )/(x -1)^8. - Colin Barker, Nov 18 2012

Mathematica

CoefficientList[Series[(x^8 + 568 x^7 + 5852 x^6 + 18888 x^5 + 23750 x^4 + 12040 x^3 + 2268 x^2 + 120 x + 1)/(x - 1)^8, {x, 0, 30}], x] (* Vincenzo Librandi, Oct 17 2013 *)

Prog

(Magma) [1] cat [(3968*n^7-6720*n^6+35840*n^5-36960*n^4+60032*n^3 -26880*n^2+11040*n)/315: n in [1..30]]; // Vincenzo Librandi, Oct 17 2013

Crossrefs

Sequence in context: A297613 A250565 A264383 * A269001 A191899 A191495

Adjacent sequences: A022147 A022148 A022149 * A022151 A022152 A022153

Keyword

nonn,easy

Author

mbaake(AT)sunelc3.tphys.physik.uni-tuebingen.de (Michael Baake)

Status

approved