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A169365 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169365 #12 Mar 17 2025 09:16:10
%S A169365 1,16,240,3600,54000,810000,12150000,182250000,2733750000,41006250000,
%T A169365 615093750000,9226406250000,138396093750000,2075941406250000,
%U A169365 31139121093750000,467086816406250000,7006302246093750000
%N A169365 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169365 The initial terms coincide with those of A170735, although the two sequences are eventually different.
%C A169365 First disagreement at index 31: a(31) = 3068016947726145386695861816406249880, A170735(31) = 3068016947726145386695861816406250000. - _Klaus Brockhaus_, Jun 17 2011
%C A169365 Computed with Magma using commands similar to those used to compute A154638.
%H A169365 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, -105).
%F A169365 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)/(105*t^31 - 14*t^30 - 14*t^29 - 14*t^28 - 14*t^27 - 14*t^26 - 14*t^25 - 14*t^24 - 14*t^23 - 14*t^22 - 14*t^21 - 14*t^20 - 14*t^19 - 14*t^18 - 14*t^17 - 14*t^16 - 14*t^15 - 14*t^14 - 14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1).
%t A169365 coxG[{31,105,-14}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Mar 17 2025 *)
%Y A169365 Cf. A170735 (G.f.: (1+x)/(1-15*x)).
%K A169365 nonn
%O A169365 0,2
%A A169365 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009