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A169105 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.

%I A169105 #10 May 17 2019 12:45:46
%S A169105 1,44,1892,81356,3498308,150427244,6468371492,278139974156,
%T A169105 11960018888708,514280812214444,22114074925221092,950905221784506956,
%U A169105 40888924536733799108,1758223755079553361644,75603621468420794550692
%N A169105 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
%C A169105 The initial terms coincide with those of A170763, although the two sequences are eventually different.
%C A169105 First disagreement at index 25: a(25) = 70257972111955573760715955540655932962298, A170763(25) = 70257972111955573760715955540655932963244. - Klaus Brockhaus, Apr 25 2011
%C A169105 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169105 <a href="/index/Rec#order_25">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, -903).
%F A169105 G.f.: (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^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 A169105 coxG[{25,903,-42}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 17 2019 *)
%Y A169105 Cf. A170763 (G.f.: (1+x)/(1-43*x)).
%K A169105 nonn
%O A169105 0,2
%A A169105 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009