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Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
0

%I #13 Mar 23 2020 02:20:40

%S 1,16,240,3600,53880,806400,12069120,180633600,2703470280,40461750000,

%T 605574696720,9063392310000,135648138214680,2030190989349600,

%U 30385049935084320,454760790684530400,6806221388012959080,101865971146974325200,1524586916316221551920

%N Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

%C The initial terms coincide with those of A170735, 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 (14,14,14,-105).

%F G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(105*t^4 - 14*t^3 - 14*t^2 - 14*t + 1).

%t CoefficientList[ Series[(t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(105*t^4 - 14*t^3 - 14*t^2 - 14*t + 1), {t, 0, 16}], t] (* _Jean-François Alcover_, Nov 26 2013 *)

%o (PARI) Vec((t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(105*t^4 - 14*t^3 - 14*t^2 - 14*t + 1) + O(t^20)) \\ _Jinyuan Wang_, Mar 23 2020

%K nonn

%O 0,2

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

%E More terms from _Jinyuan Wang_, Mar 23 2020