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 A165445 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I. 1
 1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743201, 146596599314100, 3811511581929675, 99099301124011500, 2576581829064137700, 66991127551503386400, 1741769316230819007600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The initial terms coincide with those of A170746, 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..700 Index entries for linear recurrences with constant coefficients, signature (25,25,25,25,25,25,25,25,-325). FORMULA G.f.: (t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(325*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1). MAPLE seq(coeff(series((x^9+2*x^8+2*x^7+2*x^6+2*x^5+2*x^4+2*x^3+2*x^2+2*x+1 )/(325*x^9-25*x^8-25*x^7-25*x^6-25*x^5-25*x^4-25*x^3-25*x^2 -25*x +1), x, n+1), x, n), n = 0 .. 15); # Muniru A Asiru, Oct 21 2018 MATHEMATICA coxG[{9, 325, -25}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 21 2017 *) CoefficientList[Series[(1+t)*(1-t^9)/(1-26*t+350*t^9-325*t^10), {t, 0, 20}], t] (* G. C. Greubel, Oct 20 2018 *) PROG (PARI) t='t+O('t^20); Vec((1+t)*(1-t^9)/(1-26*t+350*t^9-325*t^10)) \\ G. C. Greubel, Oct 20 2018 (Magma) R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^9)/(1-26*t+350*t^9-325*t^10) )); // G. C. Greubel, Oct 20 2018 (Sage) def A165445_list(prec): P. = PowerSeriesRing(ZZ, prec) return P((1+t)*(1-t^9)/(1-26*t+350*t^9-325*t^10)).list() A165445_list(20) # G. C. Greubel, Sep 16 2019 (GAP) a:=[27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743201];; for n in [10..20] do a[n]:=25*Sum([1..8], j-> a[n-j]) -325*a[n-9]; od; Concatenation([1], a); # G. C. Greubel, Sep 16 2019 CROSSREFS Sequence in context: A164017 A164644 A164969 * A165979 A166421 A166614 Adjacent sequences: A165442 A165443 A165444 * A165446 A165447 A165448 KEYWORD nonn,easy AUTHOR John Cannon and N. J. A. Sloane, Dec 03 2009 STATUS approved

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Last modified December 7 10:56 EST 2023. Contains 367650 sequences. (Running on oeis4.)