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%I #17 Sep 08 2022 08:45:46
%S 1,38,1406,52022,1924814,71217415,2635018344,97494717024,
%T 3607268946840,133467634460304,4938253762332042,182713586854206456,
%U 6760336027236505128,250129965636431546040,9254717436709694665512
%N Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C The initial terms coincide with those of A170757, 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="/A163660/b163660.txt">Table of n, a(n) for n = 0..635</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (36, 36, 36, 36, -666).
%F G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(666*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1).
%F a(n) = 36*a(n-1)+36*a(n-2)+36*a(n-3)+36*a(n-4)-666*a(n-5). - _Wesley Ivan Hurt_, May 11 2021
%t CoefficientList[Series[(1+x)*(1-x^5)/(1-37*x+702*x^5-666*x^6), {x,0,20}], x] (* _G. C. Greubel_, Aug 01 2017 *)
%t coxG[{5, 666, -36}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 22 2019 *)
%o (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-37*x+702*x^5-666*x^6)) \\ _G. C. Greubel_, Aug 01 2017
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-37*x+702*x^5-666*x^6) )); // _G. C. Greubel_, Apr 28 2019
%o (Sage) ((1+x)*(1-x^5)/(1-37*x+702*x^5-666*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 28 2019
%o (GAP) a:=[38, 1406, 52022, 1924814, 71217415];; for n in [6..20] do a[n]:=36*(a[n-1]+a[n-2] +a[n-3]+a[n-4]) - 666*a[n-5]; od; Concatenation([1], a); # _G. C. Greubel_, Apr 28 2019
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009
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