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A163992 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

%I A163992 #16 Sep 08 2022 08:45:47
%S A163992 1,24,552,12696,292008,6716184,154471956,3552848640,81715372992,
%T A163992 1879450227072,43227278132544,994225623975936,22867148570853180,
%U A163992 525943479177652008,12096678448229129304,278223108134446896168
%N A163992 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
%C A163992 The initial terms coincide with those of A170743, although the two sequences are eventually different.
%C A163992 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163992 G. C. Greubel, <a href="/A163992/b163992.txt">Table of n, a(n) for n = 0..730</a>
%H A163992 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (22,22,22,22,22,-253).
%F A163992 G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(253*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).
%F A163992 a(n) = -253*a(n-6) + 22*Sum_{k=1..5} a(n-k). - _Wesley Ivan Hurt_, May 11 2021
%p A163992 seq(coeff(series((1+t)*(1-t^6)/(1-23*t+275*t^6-253*t^7), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Aug 11 2019
%t A163992 CoefficientList[Series[(1+t)*(1-t^6)/(1-23*t+275*t^6-253*t^7), {t,0,30}], t] (* _G. C. Greubel_, Aug 24 2017 *)
%t A163992 coxG[{6, 253, -22}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Aug 11 2019 *)
%o A163992 (PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-23*t+275*t^6-253*t^7)) \\ _G. C. Greubel_, Aug 24 2017
%o A163992 (Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-23*t+275*t^6-253*t^7) )); // _G. C. Greubel_, Aug 11 2019
%o A163992 (Sage)
%o A163992 def A163992_list(prec):
%o A163992     P.<t> = PowerSeriesRing(ZZ, prec)
%o A163992     return P((1+t)*(1-t^6)/(1-23*t+275*t^6-253*t^7)).list()
%o A163992 A163992_list(30) # _G. C. Greubel_, Aug 11 2019
%o A163992 (GAP) a:=[24, 552, 12696, 292008, 6716184, 154471956];; for n in [7..30] do a[n]:=22*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -253*a[n-6]; od; Concatenation([1], a); # _G. C. Greubel_, Aug 11 2019
%K A163992 nonn
%O A163992 0,2
%A A163992 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009