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Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
0

%I #11 Aug 16 2023 20:40:26

%S 1,25,600,14400,345300,8280000,198547500,4761000000,114164729700,

%T 2737573095600,65644673871900,1574103433035600,37745661174674100,

%U 905108843301991200,21703740051934476300,520437222249938431200

%N Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

%C The initial terms coincide with those of A170744, 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 (23,23,23,-276).

%F G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(276*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).

%t CoefficientList[Series[(t^4 + 2 t^3 + 2 t^2 + 2 t + 1)/(276 t^4 - 23 t^3 - 23 t^2 - 23 t + 1), {t, 0, 20}], t] (* _Jinyuan Wang_, Mar 23 2020 *)

%t coxG[{4,276,-23}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 16 2023 *)

%K nonn

%O 0,2

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