A163837 - OEIS

%I #20 Sep 08 2022 08:45:47

%S 1,50,2450,120050,5882450,288238825,14123642400,692055537600,

%T 33910577282400,1661611227897600,81418604280421800,

%U 3989494661371228800,195484407940615651200,9578695296400885468800,469354075590339325411200

%N Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%C The initial terms coincide with those of A170769, 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="/A163837/b163837.txt">Table of n, a(n) for n = 0..590</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (48,48,48,48,-1176).

%F G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1176*t^5 - 48*t^4 - 48*t^3 - 48*t^2 - 48*t + 1).

%F a(n) = 48*a(n-1)+48*a(n-2)+48*a(n-3)+48*a(n-4)-1176*a(n-5). - _Wesley Ivan Hurt_, May 11 2021

%p seq(coeff(series((1+t)*(1-t^5)/(1-49*t+1224*t^5-1176*t^6), t, n+1), t, n), n = 0 .. 20); # _G. C. Greubel_, Aug 09 2019

%t CoefficientList[Series[(1+t)*(1-t^5)/(1-49*t+1224*t^5-1176*t^6), {t, 0, 20}], t] (* _G. C. Greubel_, Aug 05 2017 *)

%t coxG[{5, 1176, -48}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Aug 10 2019 *)

%o (PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^5)/(1-49*t+1224*t^5-1176*t^6)) \\ _G. C. Greubel_, Aug 05 2017 *)

%o (Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^5)/(1-49*t+1224*t^5-1176*t^6) )); // _G. C. Greubel_, Aug 09 2019

%o (Sage)

%o def A163748_list(prec):

%o     P.<t> = PowerSeriesRing(ZZ, prec)

%o     return P((1+t)*(1-t^5)/(1-49*t+1224*t^5-1176*t^6)).list()

%o A163748_list(20) # _G. C. Greubel_, Aug 09 2019

%o (GAP) a:=[50,2450,120050,5882450,288238825];; for n in [6..20] do a[n]:=48*(a[n-1]+a[n-2]+a[n-3]+a[n-4]) -1176*a[n-5]; od; Concatenation([1], a); # _G. C. Greubel_, Aug 09 2019

%K nonn

%O 0,2

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