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Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
0

%I #9 Mar 22 2020 23:43:46

%S 1,14,182,2366,30667,397488,5152056,66777984,865538310,11218616136,

%T 145409328792,1884713116104,24428580744204,316629386210592,

%U 4103970233205024,53193330778861728,689461735481280216,8936411345795737440,115828687266480560736,1501305644372339725920

%N Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

%C The initial terms coincide with those of A170733, 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_04">Index entries for linear recurrences with constant coefficients</a>, signature (12,12,12,-78).

%F G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(78*t^4 - 12*t^3 - 12*t^2 - 12*t + 1).

%t CoefficientList[ Series[(t^4 + 2 t^3 + 2 t^2 + 2 t + 1)/(78 t^4 - 12 t^3 - 12 t^2 - 12 t + 1), {t, 0, 20}], t] (* _Jinyuan Wang_, Mar 22 2020 *)

%K nonn

%O 0,2

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

%E More terms from _Jinyuan Wang_, Mar 22 2020