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URL: https://oeis.org/A022147

⇱ A022147 - OEIS

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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, 15970450, 18592130, 21524162, 24790130, 28414482, 32422530
OFFSET
0,2
LINKS
M. Baake and U. Grimm, Coordination sequences for root lattices and related graphs, arXiv:cond-mat/9706122 [cond-mat.stat-mech], 1997; Zeit. f. Kristallographie, 212 (1997), 253-256.
Roland 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
Row n=5 of A108998.
Sequence in context: A164757 A189415 A128954 * A285044 A187669 A366831
KEYWORD
nonn,easy
AUTHOR
Michael Baake (mbaake(AT)sunelc3.tphys.physik.uni-tuebingen.de)
STATUS
approved