A168700 - OEIS

%I #13 Jun 18 2024 17:45:39

%S 1,23,506,11132,244904,5387888,118533536,2607737792,57370231424,

%T 1262145091328,27767192009216,610878224202752,13439320932460544,

%U 295665060514131968,6504631331310903296,143101889288839872512

%N Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

%C The initial terms coincide with those of A170742, although the two sequences are eventually different.

%C First disagreement at index 17: a(17) = 69261314415798498295555, A170742(17) = 69261314415798498295808. - _Klaus Brockhaus_, Mar 30 2011

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

%H G. C. Greubel, <a href="/A168700/b168700.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, -231).

%F G.f.: (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)/ (231*t^17 - 21*t^16 - 21*t^15 - 21*t^14 - 21*t^13 - 21*t^12 - 21*t^11 -21*t^10 - 21*t^9 - 21*t^8 - 21*t^7 - 21*t^6 -21*t^5 -21*t^4 -21*t^3 -21*t^2 -21*t +1).

%t CoefficientList[Series[(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)/(231*t^17 - 21*t^16 - 21*t^15 - 21*t^14 - 21*t^13 - 21*t^12 - 21*t^11 - 21*t^10 - 21*t^9 - 21*t^8 - 21*t^7 - 21*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1), {t,0,50}], t] (* _G. C. Greubel_, Aug 04 2016 *)

%t coxG[{17,231,-21}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 18 2024 *)

%Y Cf. A170742 (G.f.: (1+x)/(1-22*x)).

%K nonn

%O 0,2

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