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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 (list; graph; refs; listen; history; text; internal format)
 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 G. C. Greubel, Table of n, a(n) for n = 0..620 Index entries for linear recurrences with constant coefficients, signature (39, 39, 39, 39, -780). 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:=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 Adjacent sequences:  A163674 A163675 A163676 * A163678 A163679 A163680 KEYWORD nonn AUTHOR John Cannon and N. J. A. Sloane, Dec 03 2009 STATUS approved

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Last modified December 4 15:36 EST 2021. Contains 349526 sequences. (Running on oeis4.)