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A164091
Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
3
1, 41, 1640, 65600, 2624000, 104960000, 4198399180, 167935934400, 6717436064820, 268697390145600, 10747893507936000, 429915656401920000, 17196622899456671580, 687864781713487950000, 27514585897949409744420
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170760, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
FORMULA
G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(780*t^6 - 39*t^5 - 39*t^4 - 39*t^3 - 39*t^2 - 39*t + 1).
G.f.: (1+x)*(1-x^6)/(1 -40*x +819*x^6 -780*x^7). - G. C. Greubel, Apr 25 2019
MATHEMATICA
coxG[{6, 780, -39}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 25 2015 *)
CoefficientList[Series[(1+x)*(1-x^6)/(1-40*x+819*x^6-780*x^7), {x, 0, 20}], x] (* G. C. Greubel, Apr 25 2019 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^6)/(1-40*x+819*x^6-780*x^7)) \\ G. C. Greubel, Apr 25 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^6)/(1-40*x+819*x^6-780*x^7) )); // G. C. Greubel, Apr 25 2019
(Sage) ((1+x)*(1-x^6)/(1-40*x+819*x^6-780*x^7)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019
CROSSREFS
Sequence in context: A162878 A163224 A163677 * A164685 A165173 A165692
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved