cp's OEIS Frontend

A163954 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

%I A163954 #15 Sep 08 2022 08:45:47
%S A163954 1,10,90,810,7290,65610,590445,5313600,47818800,430336800,3872739600,
%T A163954 34852032000,313644670380,2822589491040,25401392681760,
%U A163954 228595320793440,2057202978723360,18513432737727840,166608348947205840
%N A163954 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
%C A163954 The initial terms coincide with those of A003952, although the two sequences are eventually different.
%C A163954 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163954 G. C. Greubel, <a href="/A163954/b163954.txt">Table of n, a(n) for n = 0..1000</a>
%H A163954 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (8,8,8,8,8,-36).
%F A163954 G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(36*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).
%F A163954 a(n) = -36*a(n-6) + 8*Sum_{k=1..5} a(n-k). - _Wesley Ivan Hurt_, May 11 2021
%p A163954 seq(coeff(series((1+t)*(1-t^6)/(1-9*t+44*t^6-36*t^7), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Aug 10 2019
%t A163954 CoefficientList[Series[(1+t)*(1-t^6)/(1-9*t+44*t^6-36*t^7), {t, 0, 30}], t] (* _G. C. Greubel_, Aug 13 2017 *)
%t A163954 coxG[{6, 36, -8}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Aug 10 2019 *)
%o A163954 (PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-9*t+44*t^6-36*t^7)) \\ _G. C. Greubel_, Aug 13 2017
%o A163954 (Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-9*t+44*t^6-36*t^7) )); // _G. C. Greubel_, Aug 10 2019
%o A163954 (Sage)
%o A163954 def A163954_list(prec):
%o A163954     P.<t> = PowerSeriesRing(ZZ, prec)
%o A163954     return P((1+t)*(1-t^6)/(1-9*t+44*t^6-36*t^7)).list()
%o A163954 A163954_list(30) # _G. C. Greubel_, Aug 10 2019
%o A163954 (GAP) a:=[10, 90, 810, 7290, 65610, 590445];; for n in [7..30] do a[n]:=8*(a[n-1]+a[n-2]+a[n-3]+a[n-4]+a[n-5]) -36*a[n-6]; od; Concatenation([1], a); # _G. C. Greubel_, Aug 10 2019
%K A163954 nonn
%O A163954 0,2
%A A163954 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009