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 A166075 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I. 1
 1, 31, 930, 27900, 837000, 25110000, 753300000, 22599000000, 677970000000, 20339100000000, 610172999999535, 18305189999972100, 549155699998744965, 16474670999949807900, 494240129998118005500, 14827203899932253220000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The initial terms coincide with those of A170750, 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..500 Index entries for linear recurrences with constant coefficients, signature (29,29,29,29,29,29,29,29,29,-435). FORMULA G.f.: (t^10 + 2*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)/(435*t^10 - 29*t^9 - 29*t^8 - 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1). MAPLE seq(coeff(series((1+t)*(1-t^10)/(1-30*t+464*t^10-435*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Dec 05 2019 MATHEMATICA CoefficientList[Series[(1+t)*(1-t^10)/(1-30*t+464*t^10-435*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 24 2016 *) PROG (PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-30*t+464*t^10-435*t^11)) \\ G. C. Greubel, Dec 05 2019 (Magma) R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-30*t+464*t^10-435*t^11) )); // G. C. Greubel, Dec 05 2019 (Sage) def A166075_list(prec): P. = PowerSeriesRing(ZZ, prec) return P((1+t)*(1-t^10)/(1-30*t+464*t^10-435*t^11)).list() A166075_list(30) # G. C. Greubel, Dec 05 2019 (GAP) a:=[31, 930, 27900, 837000, 25110000, 753300000, 22599000000, 677970000000, 20339100000000, 610172999999535];; for n in [11..30] do a[n]:=29*Sum([1..9], j-> a[n-j]) - 435*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Dec 05 2019 CROSSREFS Sequence in context: A164667 A164992 A165547 * A166425 A166618 A167084 Adjacent sequences: A166072 A166073 A166074 * A166076 A166077 A166078 KEYWORD nonn AUTHOR John Cannon and N. J. A. Sloane, Dec 03 2009 STATUS approved

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Last modified December 3 22:01 EST 2023. Contains 367540 sequences. (Running on oeis4.)