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%I #8 Nov 25 2016 12:01:16
%S 1,31,930,27900,837000,25110000,753300000,22599000000,677970000000,
%T 20339100000000,610173000000000,18305190000000000,549155700000000000,
%U 16474671000000000000,494240130000000000000,14827203900000000000000
%N Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
%C The initial terms coincide with those of A170750, although the two sequences are eventually different.
%C First disagreement at index 25: a(25) = 8755315630910999999999999999999999535, A170750(25) = 8755315630911000000000000000000000000. - Klaus Brockhaus, Apr 25 2011
%C Computed with MAGMA using commands similar to those used to compute A154638.
%H <a href="/index/Rec#order_25">Index entries for linear recurrences with constant coefficients</a>, signature (29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, -435).
%F 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)/(435*t^25 - 29*t^24 - 29*t^23 - 29*t^22 - 29*t^21 - 29*t^20 - 29*t^19 - 29*t^18 - 29*t^17 - 29*t^16 - 29*t^15 - 29*t^14 - 29*t^13 - 29*t^12 - 29*t^11 - 29*t^10 - 29*t^9 - 29*t^8 - 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1).
%Y Cf. A170750 (G.f.: (1+x)/(1-30*x)).
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009