|
%I #12 Jan 05 2022 12:25:01
%S 1,6,30,150,750,3750,18750,93750,468750,2343750,11718750,58593750,
%T 292968750,1464843750,7324218750,36621093750,183105468750,
%U 915527343750,4577636718750,22888183593750,114440917968750,572204589843750
%N Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
%C The initial terms coincide with those of A003948, although the two sequences are eventually different.
%C First disagreement at index 28: a(28) = 44703483581542968735, A003948(28) = 44703483581542968750. - _Klaus Brockhaus_, May 24 2011
%C Computed with Magma using commands similar to those used to compute A154638.
%H <a href="/index/Rec#order_28">Index entries for linear recurrences with constant coefficients</a>, signature (4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -10).
%F G.f.: (t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*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)/(10*t^28 - 4*t^27 - 4*t^26 - 4*t^25 - 4*t^24 - 4*t^23 - 4*t^22 - 4*t^21 - 4*t^20 - 4*t^19 - 4*t^18 - 4*t^17 - 4*t^16 - 4*t^15 - 4*t^14 - 4*t^13 - 4*t^12 - 4*t^11 - 4*t^10 - 4*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t + 1).
%t coxG[{28,10,-4,30}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 05 2022 *)
%Y Cf. A003948 (G.f.: (1+x)/(1-5*x)).
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009
|
