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A022147 Coordination sequence for root lattice B_5. 4
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 (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) = (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 A160336

Adjacent sequences:  A022144 A022145 A022146 * A022148 A022149 A022150

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified May 29 10:41 EDT 2020. Contains 334699 sequences. (Running on oeis4.)