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 A168825 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I. 0

%I

%S 1,4,12,36,108,324,972,2916,8748,26244,78732,236196,708588,2125764,

%T 6377292,19131876,57395628,172186884,516560652,1549681956,4649045862,

%U 13947137568,41841412656,125524237824,376572713040,1129718137824

%N Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

%C The initial terms coincide with those of A003946, although the two sequences are eventually different.

%C First disagreement at index 20: a(20) = 4649045862, A003946(20) = 4649045868. - Klaus Brockhaus, Apr 01 2011

%C Computed with MAGMA using commands similar to those used to compute A154638.

%F G.f.: (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)/(3*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).

%Y Cf. A003946 (G.f.: (1+x)/(1-3*x)).

%K nonn

%O 0,2

%A John Cannon (john(AT)maths.usyd.edu.au) and _N. J. A. Sloane_, Dec 03 2009

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