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A163290 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I. 0

%I

%S 1,50,2450,120050,5881225,288120000,14114940000,691488000000,

%T 33875854559400,1659571130851200,81302047554268800,

%U 3982970548016611200,195124905996721243200,9559128916780140902400,468299754871670360217600

%N Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

%C The initial terms coincide with those of A170769, although the two sequences are eventually different.

%C Computed with MAGMA using commands similar to those used to compute A154638.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (48, 48, 48, -1176).

%F G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1176*t^4 - 48*t^3 - 48*t^2 - 48*t + 1).

%t CoefficientList[Series[(t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1176*t^4 - 48*t^3 - 48*t^2 - 48*t + 1), {t,0,50}], t] (* or *) Join[{1}, LinearRecurrence[ {48,48,48,-1176}, {50, 2450, 120050, 5881225}, 25]] (* _G. C. Greubel_, Dec 17 2016 *)

%t coxG[{4,1176,-48}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Mar 22 2020 *)

%o (PARI) Vec((t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1176*t^4 - 48*t^3 - 48*t^2 - 48*t + 1) + O(t^50)) \\ _G. C. Greubel_, Dec 17 2016

%K nonn

%O 0,2

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

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Last modified June 16 21:55 EDT 2021. Contains 345080 sequences. (Running on oeis4.)