A022147 Coordination sequence for root lattice B_5.

1, 50, 530, 2562, 8130, 20082, 42130, 78850, 135682, 218930, 335762, 494210, 703170, 972402, 1312530, 1735042, 2252290, 2877490, 3624722, 4508930, 5545922, 6752370, 8145810, 9744642, 11568130, 13636402

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.

Formula

a(0) = 1; for n>0, a(n) = (108*n^4 - 88*n^3 + 156*n^2 - 32*n + 6)/3 . - Philippe Deléham, Feb 20 2004

G.f.: (1+45*x+290*x^2+402*x^3+125*x^4+x^5)/(1-x)^5 = 1+2*x*(25+140*x+206*x^2+60*x^3+x^4)/(1-x)^5. - Colin Barker, Apr 13 2012

Mathematica

CoefficientList[Series[(1+45*x+290*x^2+402*x^3+125*x^4+ x^5)/(1-x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 20 2012 *)

Prog

(Magma) [1] cat[(108*n^4 - 88*n^3 + 156*n^2 - 32*n + 6)/3 : n in [1..40]]; // Vincenzo Librandi, Apr 20 2012

Crossrefs

Sequence in context: A164757 A189415 A128954 * A285044 A187669 A366831

Adjacent sequences: A022144 A022145 A022146 * A022148 A022149 A022150

Keyword

nonn,easy

Author

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

Status

approved