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A022148 Coordination sequence for root lattice B_6. 4
1, 72, 1072, 6968, 28320, 85992, 214864, 467544, 918080, 1665672, 2838384, 4596856, 7138016, 10698792, 15559824, 22049176, 30546048, 41484488, 55357104, 72718776, 94190368, 120462440, 152298960 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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) = (8*n/15)*(58*n^4 - 65*n^3 + 180*n^2 - 85*n + 47) . - Philippe Deléham, Feb 20 2004
G.f.: (1+66*x+655*x^2+1596*x^3+1167*x^4+226*x^5+x^6)/(1-x)^6 = 1+8*x*(9+80*x+202*x^2+144*x^3+29*x^4)/(1-x)^6. - Colin Barker, Apr 13 2012
MATHEMATICA
CoefficientList[Series[(1+66*x+655*x^2+1596*x^3+1167*x^4+ 226*x^5+x^6)/(1-x)^6, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 20 2012 *)
PROG
(Magma) [1] cat[(8*n/15)*(58*n^4 - 65*n^3 + 180*n^2 - 85*n + 47) : n in [1..40]]; // Vincenzo Librandi, Apr 20 2012
CROSSREFS
Sequence in context: A250650 A008399 A232573 * A192847 A064567 A269088
KEYWORD
nonn,easy
AUTHOR
mbaake(AT)sunelc3.tphys.physik.uni-tuebingen.de (Michael Baake)
STATUS
approved

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Last modified March 28 07:33 EDT 2024. Contains 371235 sequences. (Running on oeis4.)