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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

REFERENCES

R. Bacher, P. de la Harpe and B. Venkov, Series de croissance et series d'Ehrhart associees aux reseaux de racines, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142.

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.

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

Adjacent sequences:  A022145 A022146 A022147 * A022149 A022150 A022151

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified May 30 19:05 EDT 2020. Contains 334729 sequences. (Running on oeis4.)