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A170486 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.

%I A170486 #6 Nov 21 2016 17:07:26
%S A170486 1,45,1980,87120,3833280,168664320,7421230080,326534123520,
%T A170486 14367501434880,632170063134720,27815482777927680,1223881242228817920,
%U A170486 53850774658067988480,2369434084954991493120,104255099738019625697280
%N A170486 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
%C A170486 The initial terms coincide with those of A170764, although the two sequences are eventually different.
%C A170486 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170486 <a href="/index/Rec#order_45">Index entries for linear recurrences with constant coefficients</a>, signature (43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, -946).
%F A170486 G.f. (t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 +
%F A170486 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 +
%F A170486 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 +
%F A170486 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 +
%F A170486 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 +
%F A170486 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(946*t^45 - 43*t^44 - 43*t^43 -
%F A170486 43*t^42 - 43*t^41 - 43*t^40 - 43*t^39 - 43*t^38 - 43*t^37 - 43*t^36 -
%F A170486 43*t^35 - 43*t^34 - 43*t^33 - 43*t^32 - 43*t^31 - 43*t^30 - 43*t^29 -
%F A170486 43*t^28 - 43*t^27 - 43*t^26 - 43*t^25 - 43*t^24 - 43*t^23 - 43*t^22 -
%F A170486 43*t^21 - 43*t^20 - 43*t^19 - 43*t^18 - 43*t^17 - 43*t^16 - 43*t^15 -
%F A170486 43*t^14 - 43*t^13 - 43*t^12 - 43*t^11 - 43*t^10 - 43*t^9 - 43*t^8 -
%F A170486 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1)
%K A170486 nonn
%O A170486 0,2
%A A170486 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009