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A169249 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.

%I A169249 #10 May 10 2018 02:38:28
%S A169249 1,44,1892,81356,3498308,150427244,6468371492,278139974156,
%T A169249 11960018888708,514280812214444,22114074925221092,950905221784506956,
%U A169249 40888924536733799108,1758223755079553361644,75603621468420794550692
%N A169249 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
%C A169249 The initial terms coincide with those of A170763, although the two sequences are eventually different.
%C A169249 First disagreement at index 28: a(28) = 5586000588705251802993243477170931262108639762, A170763(28) = 5586000588705251802993243477170931262108640708. - _Klaus Brockhaus_, May 24 2011
%C A169249 Computed with Magma using commands similar to those used to compute A154638.
%H A169249 <a href="/index/Rec#order_28">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, -903).
%F A169249 G.f.: (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^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).
%Y A169249 Cf. A170763 (G.f.: (1+x)/(1-43*x)).
%K A169249 nonn
%O A169249 0,2
%A A169249 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009