A022149 Coordination sequence for root lattice B_7.

1, 98, 1946, 16394, 83442, 307314, 907018, 2282394, 5095650, 10368386, 19594106, 34866218, 59021522, 95799186, 150015210, 227752378, 336565698, 485703330, 686343002, 951843914, 1298014130, 1743393458

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 (7,-21,35,-35,21,-7,1).

Formula

a(0) = 1; for n>0, a(n) = (968*n^6 - 1368*n^5 + 5420*n^4 - 4080*n^3 + 4232*n^2 - 852*n + 90)/45 . - Philippe Deléham, Feb 20 2004

G.f.: -(x^7+371*x^6+2793*x^5+6155*x^4+4795*x^3+1281*x^2+91*x+1)/(x-1)^7 = 1 +2*x*(x+1) *(49+581*x+1834*x^2+1226*^2+181*x^4+x^5) /(1-x)^7. - Colin Barker, Nov 18 2012

Mathematica

CoefficientList[Series[-(x^7 + 371 x^6 + 2793 x^5 + 6155 x^4 + 4795 x^3 + 1281 x^2 + 91 x + 1)/(x - 1)^7, {x, 0, 30}], x] (* Vincenzo Librandi, Oct 16 2013 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 98, 1946, 16394, 83442, 307314, 907018, 2282394}, 30] (* Harvey P. Dale, Nov 20 2018 *)

Crossrefs

Sequence in context: A019563 A285045 A197616 * A128801 A188484 A271037

Adjacent sequences: A022146 A022147 A022148 * A022150 A022151 A022152

Keyword

nonn,easy

Author

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

Status

approved