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%I A164639 #12 Feb 22 2024 14:41:21
%S A164639 1,26,650,16250,406250,10156250,253906250,6347655925,158691390000,
%T A164639 3967284547200,99182108610000,2479552588500000,61988811543750000,
%U A164639 1549720209375000000,38743003253906355300,968575031835945300000
%N A164639 Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.
%C A164639 The initial terms coincide with those of A170745, although the two sequences are eventually different.
%C A164639 Computed with MAGMA using commands similar to those used to compute A154638.
%H A164639 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (24,24,24,24,24,24,-300).
%F A164639 G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(300*t^7 - 24*t^6 - 24*t^5 - 24*t^4 - 24*t^3 - 24*t^2 - 24*t + 1).
%t A164639 coxG[{7,300,-24}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Feb 04 2015 *)
%K A164639 nonn
%O A164639 0,2
%A A164639 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009

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