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A169372 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169372 #12 May 08 2018 00:33:28
%S A169372 1,23,506,11132,244904,5387888,118533536,2607737792,57370231424,
%T A169372 1262145091328,27767192009216,610878224202752,13439320932460544,
%U A169372 295665060514131968,6504631331310903296,143101889288839872512
%N A169372 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169372 The initial terms coincide with those of A170742, although the two sequences are eventually different.
%C A169372 First disagreement at index 31: a(31) = 430931519457788077189834416858879651479299, A170742(31) = 430931519457788077189834416858879651479552. - _Klaus Brockhaus_, Jun 17 2011
%C A169372 Computed with Magma using commands similar to those used to compute A154638.
%H A169372 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, -231).
%F A169372 G.f.: (t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*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)/(231*t^31 - 21*t^30 - 21*t^29 - 21*t^28 - 21*t^27 - 21*t^26 - 21*t^25 - 21*t^24 - 21*t^23 - 21*t^22 - 21*t^21 - 21*t^20 - 21*t^19 - 21*t^18 - 21*t^17 - 21*t^16 - 21*t^15 - 21*t^14 - 21*t^13 - 21*t^12 - 21*t^11 - 21*t^10 - 21*t^9 - 21*t^8 - 21*t^7 - 21*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1).
%t A169372 coxG[{31,231,-21}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 28 2015 *)
%Y A169372 Cf. A170742 (G.f.: (1+x)/(1-22*x)).
%K A169372 nonn
%O A169372 0,2
%A A169372 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009