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Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.
0

%I #6 Nov 23 2016 22:06:49

%S 1,8,56,392,2744,19208,134456,941192,6588344,46118380,322828464,

%T 2259797904,15818575920,110729965584,775109298096,5425761859728,

%U 37980310429488,265862014886160,1861032997362084,13027223233652040

%N Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

%C The initial terms coincide with those of A003950, 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 (6, 6, 6, 6, 6, 6, 6, 6, -21).

%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)/(21*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t

%F + 1)

%K nonn

%O 0,2

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