A163745 - OEIS

%I #18 Dec 03 2025 17:11:30

%S 1,43,1806,75852,3185784,133802025,5619647124,236023587219,

%T 9912923799660,416339991317124,17486161688852682,734413837213650321,

%U 30845173108213815708,1295488532304021561975,54410151353124129064362

%N Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%C The initial terms coincide with those of A170762, 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="/A163745/b163745.txt">Table of n, a(n) for n = 0..614</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (41, 41, 41, 41, -861).

%F G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(861*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).

%F a(n) = 41*a(n-1)+41*a(n-2)+41*a(n-3)+41*a(n-4)-861*a(n-5). - _Wesley Ivan Hurt_, May 11 2021

%p seq(coeff(series((1+t)*(1-t^5)/(1-42*t+902*t^5-861*t^6), t, n+1), t, n), n = 0 .. 20); # _G. C. Greubel_, Aug 09 2019

%t CoefficientList[Series[(1+t)*(1-t^5)/(1-42*t+902*t^5-861*t^6), {t, 0, 20}], t] (* _G. C. Greubel_, Aug 02 2017 *)

%t coxG[{5, 865, -41}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Aug 09 2019 *)

%o (PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^5)/(1-42*t+902*t^5-861*t^6)) \\ _G. C. Greubel_, Aug 02 2017

%o (Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^5)/(1-42*t+902*t^5-861*t^6) )); // _G. C. Greubel_, Aug 09 2019

%o (SageMath)

%o def A163745_list(prec):

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

%o     return P((1+t)*(1-t^5)/(1-42*t+902*t^5-861*t^6)).list()

%o A163745_list(20) # _G. C. Greubel_, Aug 09 2019

%K nonn

%O 0,2

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