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A163962
Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
2
1, 15, 210, 2940, 41160, 576240, 8067255, 112940100, 1581140925, 22135686300, 309895595100, 4338482148000, 60737963515320, 850320477564285, 11904332524792890, 166658497119549435, 2333188744879254990
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170734, 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)/(91*t^6 - 13*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1).
G.f.: (1+x)*(1-x^6)/(1 -14*x +104*x^6 -91*x^7). - G. C. Greubel, Apr 25 2019
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^6)/(1-14*x+104*x^6-91*x^7), {x, 0, 20}], x] (* G. C. Greubel, Aug 13 2017, modified Apr 25 2019 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^6)/(1-14*x+104*x^6-91*x^7)) \\ G. C. Greubel, Aug 13 2017, modified Apr 25 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^6)/(1-14*x+104*x^6-91*x^7) )); // G. C. Greubel, Apr 25 2019
(Sage) ((1+x)*(1-x^6)/(1-14*x+104*x^6-91*x^7)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019
CROSSREFS
Sequence in context: A076139 A163091 A163440 * A164626 A164860 A165282
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved