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Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
0

%I #10 Jul 09 2024 19:17:08

%S 1,26,650,16250,405925,10140000,253297200,6327360000,158057355300,

%T 3948270300000,98627731207200,2463719204700000,61543667742382800,

%U 1537359871188960000,38403225875902867200,959311990194611040000

%N Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

%C The initial terms coincide with those of A170745, 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 (24,24,24,-300).

%F G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(300*t^4 - 24*t^3 - 24*t^2 - 24*t + 1).

%t coxG[{4,300,-24}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 09 2024 *)

%o (PARI) Vec((t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(300*t^4 - 24*t^3 - 24*t^2 - 24*t + 1) + O(t^20)) \\ _Jinyuan Wang_, Mar 23 2020

%K nonn

%O 0,2

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