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A168961 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.

%I A168961 #10 Nov 25 2016 10:07:31
%S A168961 1,44,1892,81356,3498308,150427244,6468371492,278139974156,
%T A168961 11960018888708,514280812214444,22114074925221092,950905221784506956,
%U A168961 40888924536733799108,1758223755079553361644,75603621468420794550692
%N A168961 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
%C A168961 The initial terms coincide with those of A170763, although the two sequences are eventually different.
%C A168961 First disagreement at index 22: a(22) = 883670269434836854122479222466648946, A170763(22) = 883670269434836854122479222466649892. - Klaus Brockhaus, Apr 10 2011
%C A168961 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168961 <a href="/index/Rec#order_22">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, -903).
%F A168961 G.f.: (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^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 A168961 coxG[{22,903,-42}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 09 2016 *)
%Y A168961 Cf. A170763 (G.f.: (1+x)/(1-43*x)).
%K A168961 nonn
%O A168961 0,2
%A A168961 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009