A163962 - OEIS

%I #15 Sep 08 2022 08:45:47

%S 1,15,210,2940,41160,576240,8067255,112940100,1581140925,22135686300,

%T 309895595100,4338482148000,60737963515320,850320477564285,

%U 11904332524792890,166658497119549435,2333188744879254990

%N Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

%C The initial terms coincide with those of A170734, although the two sequences are eventually different.

%C Computed with MAGMA using commands similar to those used to compute A154638.

%H G. C. Greubel, <a href="/A163962/b163962.txt">Table of n, a(n) for n = 0..870</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (13, 13, 13, 13, 13, -91).

%F G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(91*t^6 - 13*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1).

%F G.f.: (1+x)*(1-x^6)/(1 -14*x +104*x^6 -91*x^7). - _G. C. Greubel_, Apr 25 2019

%t CoefficientList[Series[(1+x)*(1-x^6)/(1-14*x+104*x^6-91*x^7), {x, 0, 20}], x] (* _G. C. Greubel_, Aug 13 2017, modified Apr 25 2019 *)

%o (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^6)/(1-14*x+104*x^6-91*x^7)) \\ _G. C. Greubel_, Aug 13 2017, modified Apr 25 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^6)/(1-14*x+104*x^6-91*x^7) )); // _G. C. Greubel_, Apr 25 2019

%o (Sage) ((1+x)*(1-x^6)/(1-14*x+104*x^6-91*x^7)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 25 2019

%K nonn

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009