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A163969
Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
0
1, 20, 380, 7220, 137180, 2606420, 49521790, 940910400, 17877229200, 339666055200, 6453630356400, 122618507616000, 2329742730783510, 44264942521047180, 841030689999256020, 15979521970107624780
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170739, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
FORMULA
G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(171*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1).
MATHEMATICA
coxG[{6, 171, -18}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 21 2015 *)
CoefficientList[Series[(t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(171*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 23 2017 *)
PROG
(PARI) t='t+O('t^50); Vec((t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(171*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1)) \\ G. C. Greubel, Aug 23 2017
CROSSREFS
Sequence in context: A342886 A163124 A163454 * A164633 A164911 A165348
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved