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Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
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%I #10 Mar 23 2020 09:48:16

%S 1,21,420,8400,167790,3351600,66948210,1337288400,26712295890,

%T 533577313500,10658190898110,212897044846500,4252612111884990,

%U 84945799915397400,1696789816099808010,33893325895893882600,677018172425014524090,13523417772619230573300

%N Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

%C The initial terms coincide with those of A170740, 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 (19,19,19,-190).

%F G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(190*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).

%t coxG[{4,190,-19}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Mar 25 2019 *)

%o (PARI) Vec((t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(190*t^4 - 19*t^3 - 19*t^2 - 19*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