cp's OEIS Frontend

A165979 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

%I A165979 #15 Sep 08 2022 08:45:48
%S A165979 1,27,702,18252,474552,12338352,320797152,8340725952,216858874752,
%T A165979 5638330743552,146596599332001,3811511582622900,99099301147958475,
%U A165979 2576581829840760300,66991127575699606500,1741769316964025575200
%N A165979 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C A165979 The initial terms coincide with those of A170746, although the two sequences are eventually different.
%C A165979 Computed with MAGMA using commands similar to those used to compute A154638.
%H A165979 G. C. Greubel, <a href="/A165979/b165979.txt">Table of n, a(n) for n = 0..500</a>
%H A165979 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (25, 25, 25, 25, 25, 25, 25, 25, 25, -325).
%F A165979 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)/(325*t^10 - 25*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).
%F A165979 G.f.: (1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11). - _G. C. Greubel_, Apr 26 2019
%t A165979 CoefficientList[Series[(1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11), {x, 0, 20}], x] (* _G. C. Greubel_, Apr 20 2016, modified Apr 26 2019 *)
%t A165979 coxG[{10, 325, -25}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Apr 26 2019 *)
%o A165979 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11)) \\ _G. C. Greubel_, Apr 26 2019
%o A165979 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11) )); // _G. C. Greubel_, Apr 26 2019
%o A165979 (Sage) ((1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 26 2019
%K A165979 nonn
%O A165979 0,2
%A A165979 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009