cp's OEIS Frontend

A163835 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%I A163835 #24 Sep 08 2022 08:45:47
%S A163835 1,49,2352,112896,5419008,260111208,12485281536,599290805400,
%T A163835 28765828659456,1380753535666176,66275870193948072,
%U A163835 3181227392509145280,152698224757140201048,7329481664494083280704,351813529958166317583360
%N A163835 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C A163835 The initial terms coincide with those of A170768, although the two sequences are eventually different.
%C A163835 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163835 G. C. Greubel, <a href="/A163835/b163835.txt">Table of n, a(n) for n = 0..590</a>
%H A163835 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (47,47,47,47,-1128).
%F A163835 G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1128*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).
%F A163835 a(n) = 47*a(n-1)+47*a(n-2)+47*a(n-3)+47*a(n-4)-1128*a(n-5). - _Wesley Ivan Hurt_, May 11 2021
%p A163835 seq(coeff(series((1+t)*(1-t^5)/(1-48*t+1175*t^5-1128*t^6), t, n+1), t, n), n = 0 .. 20); # _G. C. Greubel_, Aug 09 2019
%t A163835 CoefficientList[Series[(1+t)*(1-t^5)/(1-48*t+1175*t^5-1128*t^6), {t, 0, 20}], t] (* _G. C. Greubel_, Aug 05 2017 *)
%t A163835 coxG[{5,1128,-47}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 10 2019 *)
%o A163835 (PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^5)/(1-48*t+1175*t^5-1128*t^6)) \\ _G. C. Greubel_, Aug 05 2017
%o A163835 (Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^5)/(1-48*t+1175*t^5-1128*t^6) )); // _G. C. Greubel_, Aug 09 2019
%o A163835 (Sage)
%o A163835 def A163835_list(prec):
%o A163835     P.<t> = PowerSeriesRing(ZZ, prec)
%o A163835     return P((1+t)*(1-t^5)/(1-48*t+1175*t^5-1128*t^6)).list()
%o A163835 A163835_list(20) # _G. C. Greubel_, Aug 09 2019
%o A163835 (GAP) a:=[49,2352,112896,5419008,260111208];; for n in [6..20] do a[n]:=47*(a[n-1]+a[n-2]+a[n-3]+a[n-4]) -1128*a[n-5]; od; Concatenation([1], a); # _G. C. Greubel_, Aug 09 2019
%K A163835 nonn
%O A163835 0,2
%A A163835 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009