A022152 Coordination sequence for root lattice B_10.

1, 200, 7760, 122264, 1099040, 6728168, 31208560, 117555640, 376977472, 1064088840, 2708805776, 6332774360, 13786237280, 28250329640, 54959921840, 102213292024, 182747113600, 315568484680, 528350005968, 860509231640, 1367110174112, 2123741938280, 3232547993840

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, 1997; 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 (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

a(0)=1; for n>0, a(n) = ( 2704*n^9 - 6024*n^8 + 51648*n^7 - 80976*n^6 + 248304*n^5 - 239736*n^4 + 296672*n^3 - 126864*n^2 + 43272*n ) / 945. - Ralf Stephan, Apr 28 2004

G.f.: (x^10 +1150*x^9 +19629*x^8 +114600*x^7 +291410*x^6 +350196*x^5 +201810*x^4 +53544*x^3 +5805*x^2 +190*x +1) / (x -1)^10. - Colin Barker, Nov 18 2012

Mathematica

CoefficientList[Series[(x^10 + 1150 x^9 + 19629 x^8 + 114600 x^7 + 291410 x^6 + 350196 x^5 + 201810 x^4 + 53544 x^3 + 5805 x^2 + 190 x + 1)/(x - 1)^10, {x, 0, 30}], x] (* Vincenzo Librandi, Oct 17 2013 *)
LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {1, 200, 7760, 122264, 1099040, 6728168, 31208560, 117555640, 376977472, 1064088840, 2708805776}, 30] (* Harvey P. Dale, Sep 16 2019 *)

Prog

(Magma) [1] cat [(2704*n^9-6024*n^8+51648*n^7-80976*n^6+248304*n^5-239736*n^4+296672*n^3 -126864*n^2+43272*n)/945: n in [1..30]]; // Vincenzo Librandi, Oct 17 2013

Crossrefs

Sequence in context: A199534 A035747 A219414 * A249238 A230966 A221039

Adjacent sequences: A022149 A022150 A022151 * A022153 A022154 A022155

Keyword

nonn,easy

Author

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

Status

approved