A168873 - OEIS

%I #11 Dec 03 2025 17:11:32

%S 1,4,12,36,108,324,972,2916,8748,26244,78732,236196,708588,2125764,

%T 6377292,19131876,57395628,172186884,516560652,1549681956,4649045868,

%U 13947137598,41841412776,125524238280,376572714696,1129718143656

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

%C The initial terms coincide with those of A003946, although the two sequences are eventually different.

%C First disagreement at index 21: a(21) = 13947137598, A003946(21) = 13947137604. - Klaus Brockhaus, Apr 04 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 (2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -3).

%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)/(3*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).

%t coxG[{21,3,-2,30}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 04 2017 *)

%Y Cf. A003946 (G.f.: (1+x)/(1-3*x)).

%K nonn

%O 0,2

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