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Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.
0

%I #8 May 06 2018 15:50:48

%S 1,20,380,7220,137180,2606420,49521980,940917620,17877434780,

%T 339671260630,6453753948360,122621324950440,2329805172758760,

%U 44266298257724040,841059666427601160,15980133653210465640

%N Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

%C The initial terms coincide with those of A170739, although the two sequences are eventually different.

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

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (18, 18, 18, 18, 18, 18, 18, 18, -171).

%F G.f. (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 +

%F 1)/(171*t^9 - 18*t^8 - 18*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 -

%F 18*t^2 - 18*t + 1)

%t coxG[{9,171,-18}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 06 2018 *)

%K nonn

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009