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A163677
Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
1
1, 41, 1640, 65600, 2624000, 104959180, 4198334400, 167932064820, 6717230145600, 268687107936000, 10747400402591580, 429892659535950000, 17195572119777744420, 687817514366631090000, 27512485759363357584000
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.
FORMULA
G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(780*t^5 - 39*t^4 - 39*t^3 - 39*t^2 - 39*t + 1).
a(n) = 39*a(n-1)+39*a(n-2)+39*a(n-3)+39*a(n-4)-780*a(n-5). - Wesley Ivan Hurt, May 11 2021
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^5)/(1-40*x+819*x^5-780*x^6), {x, 0, 20}], x] (* G. C. Greubel, Aug 02 2017 *)
coxG[{5, 780, -39}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 24 2019 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-40*x+819*x^5-780*x^6)) \\ G. C. Greubel, Aug 02 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-40*x+819*x^5-780*x^6) )); // G. C. Greubel, May 24 2019
(Sage) ((1+x)*(1-x^5)/(1-40*x+819*x^5-780*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 24 2019
CROSSREFS
Sequence in context: A281608 A162878 A163224 * A164091 A164685 A165173
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved