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A163345 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%I A163345 #18 Sep 08 2022 08:45:46
%S A163345 1,7,42,252,1512,9051,54180,324345,1941660,11623500,69582660,
%T A163345 416548125,2493614550,14927719275,89362970550,534960522600,
%U A163345 3202475913000,19171231408875,114766238286000,687034086094125,4112845750671000
%N A163345 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C A163345 The initial terms coincide with those of A003949, although the two sequences are eventually different.
%C A163345 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163345 G. C. Greubel, <a href="/A163345/b163345.txt">Table of n, a(n) for n = 0..1000</a>
%H A163345 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5, 5, 5, 5, -15).
%F A163345 G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(15*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1).
%F A163345 a(n) = 5*a(n-1)+5*a(n-2)+5*a(n-3)+5*a(n-4)-15*a(n-5). - _Wesley Ivan Hurt_, May 10 2021
%t A163345 CoefficientList[Series[(1+x)*(1-x^5)/(1-6*x+20*x^5-15*x^6), {x, 0, 30}], x] (* or *) LinearRecurrence[{5,5,5,5,-15}, {1,7,42,252,1512,9051}, 30] (* _G. C. Greubel_, Dec 19 2016 *)
%t A163345 coxG[{5,15,-5}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 09 2018 *)
%o A163345 (PARI) my(x='x+O('x^30)); Vec((1+x)*(1-x^5)/(1-6*x+20*x^5-15*x^6)) \\ _G. C. Greubel_, Dec 19 2016
%o A163345 (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-6*x+20*x^5-15*x^6) )); // _G. C. Greubel_, May 12 2019
%o A163345 (Sage) ((1+x)*(1-x^5)/(1-6*x+20*x^5-15*x^6)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 12 2019
%K A163345 nonn,easy
%O A163345 0,2
%A A163345 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009