cp's OEIS Frontend

A168875 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.

%I A168875 #8 Nov 25 2016 09:32:29
%S A168875 1,6,30,150,750,3750,18750,93750,468750,2343750,11718750,58593750,
%T A168875 292968750,1464843750,7324218750,36621093750,183105468750,
%U A168875 915527343750,4577636718750,22888183593750,114440917968750,572204589843735
%N A168875 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
%C A168875 The initial terms coincide with those of A003948, although the two sequences are eventually different.
%C A168875 First disagreement at index 21: a(21) = 572204589843735, A003948(21) = 572204589843750 . - Klaus Brockhaus, Apr 04 2011
%C A168875 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168875 <a href="/index/Rec#order_21">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, -10).
%F A168875 G.f.: (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^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 A168875 Cf. A003948 (G.f.: (1+x)/(1-5*x)).
%K A168875 nonn
%O A168875 0,2
%A A168875 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009