A163451 - OEIS

%I #16 Sep 08 2022 08:45:46

%S 1,17,272,4352,69632,1113976,17821440,285108360,4561178880,

%T 72969984000,1167377713080,18675771192000,298775988016200,

%U 4779834262113600,76468044587443200,1223339873805905400,19571056837109136000

%N Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%C The initial terms coincide with those of A170736, 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="/A163451/b163451.txt">Table of n, a(n) for n = 0..825</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (15, 15, 15, 15, -120).

%F G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(120*t^5 - 15*t^4 - 15*t^3 - 15*t^2 - 15*t + 1).

%F a(n) = 15*a(n-1)+15*a(n-2)+15*a(n-3)+15*a(n-4)-120*a(n-5). - _Wesley Ivan Hurt_, May 10 2021

%t CoefficientList[Series[(1+x)*(1-x^5)/(1-16*x+135*x^5-120*x^6), {x, 0, 20}], x] (* _G. C. Greubel_, Dec 24 2016 *)

%t coxG[{5, 120, -15}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 13 2019 *)

%o (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-16*x+135*x^5-120*x^6)) \\ _G. C. Greubel_, Dec 24 2016

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-16*x+135*x^5-120*x^6) )); // _G. C. Greubel_, May 13 2019

%o (Sage) ((1+x)*(1-x^5)/(1-16*x+135*x^5-120*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 13 2019

%K nonn

%O 0,2

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