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A169367 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169367 #12 Aug 28 2022 14:00:40
%S A169367 1,18,306,5202,88434,1503378,25557426,434476242,7386096114,
%T A169367 125563633938,2134581776946,36287890208082,616894133537394,
%U A169367 10487200270135698,178282404592306866,3030800878069216722,51523614927176684274
%N A169367 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169367 The initial terms coincide with those of A170737, although the two sequences are eventually different.
%C A169367 First disagreement at index 31: a(31) = 147482383064665780017972018518259939129, A170737(31) = 147482383064665780017972018518259939282. - _Klaus Brockhaus_, Jun 17 2011
%C A169367 Computed with Magma using commands similar to those used to compute A154638.
%H A169367 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, -136).
%F A169367 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)/(136*t^31 - 16*t^30 - 16*t^29 - 16*t^28 - 16*t^27 - 16*t^26 - 16*t^25 - 16*t^24 - 16*t^23 - 16*t^22 - 16*t^21 - 16*t^20 - 16*t^19 - 16*t^18 - 16*t^17 - 16*t^16 - 16*t^15 - 16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1).
%t A169367 coxG[{31,136,-16}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 28 2022 *)
%Y A169367 Cf. A170737 (G.f.: (1+x)/(1-17*x)).
%K A169367 nonn
%O A169367 0,2
%A A169367 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009