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A169181 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.

%I A169181 #10 Nov 25 2016 13:59:22
%S A169181 1,24,552,12696,292008,6716184,154472232,3552861336,81715810728,
%T A169181 1879463646744,43227663875112,994236269127576,22867434189934248,
%U A169181 525950986368487704,12096872686475217192,278228071788929995416
%N A169181 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
%C A169181 The initial terms coincide with those of A170743, although the two sequences are eventually different.
%C A169181 First disagreement at index 27: a(27) = 6097263699699589097327944450148848260, A170743(27) = 6097263699699589097327944450148848536. - Klaus Brockhaus, May 07 2011
%C A169181 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169181 <a href="/index/Rec#order_27">Index entries for linear recurrences with constant coefficients</a>, signature (22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, -253).
%F A169181 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)/(253*t^27 - 22*t^26 - 22*t^25 - 22*t^24 - 22*t^23 - 22*t^22 - 22*t^21 - 22*t^20 - 22*t^19 - 22*t^18 - 22*t^17 - 22*t^16 - 22*t^15 - 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).
%t A169181 coxG[{27,253,-22}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 19 2015 *)
%Y A169181 Cf. A170743 (G.f.: (1+x)/(1-23*x)).
%K A169181 nonn
%O A169181 0,2
%A A169181 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009