A168890 - OEIS

%I #8 Nov 25 2016 09:37:00

%S 1,21,420,8400,168000,3360000,67200000,1344000000,26880000000,

%T 537600000000,10752000000000,215040000000000,4300800000000000,

%U 86016000000000000,1720320000000000000,34406400000000000000

%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)^21 = I.

%C The initial terms coincide with those of A170740, although the two sequences are eventually different.

%C First disagreement at index 21: a(21) = 2202009599999999999999999790, A170740(21) = 2202009600000000000000000000. - Klaus Brockhaus, Apr 05 2011

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

%H <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).

%F G.f.: (t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*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 + 1)/(190*t^21 - 19*t^20 - 19*t^19 - 19*t^18 - 19*t^17 - 19*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).

%Y Cf. A170740 (G.f.: (1+x)/(1-20*x)).

%K nonn

%O 0,2

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