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A169393 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169393 #16 Oct 11 2024 23:02:43
%S A169393 1,44,1892,81356,3498308,150427244,6468371492,278139974156,
%T A169393 11960018888708,514280812214444,22114074925221092,950905221784506956,
%U A169393 40888924536733799108,1758223755079553361644,75603621468420794550692
%N A169393 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169393 The initial terms coincide with those of A170763, although the two sequences are eventually different.
%C A169393 First disagreement at index 31: a(31) = 444126148806188455100583809139429231856471696770010, A170763(31) = 444126148806188455100583809139429231856471696770956. - _Klaus Brockhaus_, Jun 17 2011
%C A169393 Computed with Magma using commands similar to those used to compute A154638.
%H A169393 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, -903).
%F A169393 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)/(903*t^31 - 42*t^30 - 42*t^29 - 42*t^28 - 42*t^27 - 42*t^26 - 42*t^25 - 42*t^24 - 42*t^23 - 42*t^22 - 42*t^21 - 42*t^20 - 42*t^19 - 42*t^18 - 42*t^17 - 42*t^16 - 42*t^15 - 42*t^14 - 42*t^13 - 42*t^12 - 42*t^11 - 42*t^10 - 42*t^9 - 42*t^8 - 42*t^7 - 42*t^6 - 42*t^5 - 42*t^4 - 42*t^3 - 42*t^2 - 42*t + 1).
%t A169393 coxG[{31,903,-42}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 30 2024 *)
%Y A169393 Cf. A170763 (G.f.: (1+x)/(1-43*x)).
%K A169393 nonn
%O A169393 0,2
%A A169393 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009