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A169183 Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.

%I A169183 #10 May 23 2023 15:13:28
%S A169183 1,26,650,16250,406250,10156250,253906250,6347656250,158691406250,
%T A169183 3967285156250,99182128906250,2479553222656250,61988830566406250,
%U A169183 1549720764160156250,38743019104003906250,968575477600097656250
%N A169183 Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
%C A169183 The initial terms coincide with those of A170745, although the two sequences are eventually different.
%C A169183 First disagreement at index 27: a(27) = 57731597280508140102028846740722655925, A170745(27) = 57731597280508140102028846740722656250. - Klaus Brockhaus, May 07 2011
%C A169183 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169183 <a href="/index/Rec#order_27">Index entries for linear recurrences with constant coefficients</a>, signature (24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, -300).
%F A169183 G.f.: (t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(300*t^27 - 24*t^26 - 24*t^25 - 24*t^24 - 24*t^23 - 24*t^22 - 24*t^21 - 24*t^20 - 24*t^19 - 24*t^18 - 24*t^17 - 24*t^16 - 24*t^15 - 24*t^14 - 24*t^13 - 24*t^12 - 24*t^11 - 24*t^10 - 24*t^9 - 24*t^8 - 24*t^7 - 24*t^6 - 24*t^5 - 24*t^4 - 24*t^3 - 24*t^2 - 24*t + 1).
%t A169183 coxG[{27,300,-24}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 23 2023 *)
%Y A169183 Cf. A170745 (G.f.: (1+x)/(1-25*x)).
%K A169183 nonn
%O A169183 0,2
%A A169183 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009