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A169083 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.

%I A169083 #10 Jun 12 2020 15:36:19
%S A169083 1,22,462,9702,203742,4278582,89850222,1886854662,39623947902,
%T A169083 832102905942,17474161024782,366957381520422,7706105011928862,
%U A169083 161828205250506102,3398392310260628142,71366238515473190982
%N A169083 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
%C A169083 The initial terms coincide with those of A170741, although the two sequences are eventually different.
%C A169083 First disagreement at index 25: a(25) = 1190380364299996850871233051783151, A170741(25) = 1190380364299996850871233051783382. - Klaus Brockhaus, Apr 25 2011
%C A169083 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169083 <a href="/index/Rec#order_25">Index entries for linear recurrences with constant coefficients</a>, signature (20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, -210).
%F A169083 G.f.: (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)/(210*t^25 - 20*t^24 - 20*t^23 - 20*t^22 - 20*t^21 - 20*t^20 - 20*t^19 - 20*t^18 - 20*t^17 - 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).
%t A169083 coxG[{25,210,-20}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 12 2020 *)
%Y A169083 Cf. A170741 (G.f.: (1+x)/(1-21*x)).
%K A169083 nonn
%O A169083 0,2
%A A169083 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009