cp's OEIS Frontend

A169355 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169355 #10 May 10 2018 00:17:57
%S A169355 1,6,30,150,750,3750,18750,93750,468750,2343750,11718750,58593750,
%T A169355 292968750,1464843750,7324218750,36621093750,183105468750,
%U A169355 915527343750,4577636718750,22888183593750,114440917968750,572204589843750
%N A169355 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169355 The initial terms coincide with those of A003948, although the two sequences are eventually different.
%C A169355 First disagreement at index 31: a(31) = 5587935447692871093735, A003948(31) = 5587935447692871093750. - _Klaus Brockhaus_, Jun 17 2011
%C A169355 Computed with Magma using commands similar to those used to compute A154638.
%H A169355 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -10).
%F A169355 G.f.: (t^31 + 2*t^30 + 2*t^29 + 2*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)/(10*t^31 - 4*t^30 - 4*t^29 - 4*t^28 - 4*t^27 - 4*t^26 - 4*t^25 - 4*t^24 - 4*t^23 - 4*t^22 - 4*t^21 - 4*t^20 - 4*t^19 - 4*t^18 - 4*t^17 - 4*t^16 - 4*t^15 - 4*t^14 - 4*t^13 - 4*t^12 - 4*t^11 - 4*t^10 - 4*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t + 1).
%Y A169355 Cf. A003948 (G.f.: (1+x)/(1-5*x)).
%K A169355 nonn
%O A169355 0,2
%A A169355 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009