cp's OEIS Frontend

A168999 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.

%I A168999 #10 Oct 11 2021 12:38:04
%S A168999 1,34,1122,37026,1221858,40321314,1330603362,43909910946,
%T A168999 1449027061218,47817893020194,1577990469666402,52073685498991266,
%U A168999 1718431621466711778,56708243508401488674,1871372035777249126242,61755277180649221165986
%N A168999 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
%C A168999 The initial terms coincide with those of A170753, although the two sequences are eventually different.
%C A168999 First disagreement at index 23: a(23) = 86853154048726829283367181168350065, A170753(23) = 86853154048726829283367181168350626. - Klaus Brockhaus, Apr 19 2011
%C A168999 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168999 <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, -528).
%F A168999 G.f.: (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)/(528*t^23 - 32*t^22 - 32*t^21 - 32*t^20 - 32*t^19 - 32*t^18 - 32*t^17 - 32*t^16 - 32*t^15 - 32*t^14 - 32*t^13 - 32*t^12 - 32*t^11 - 32*t^10 - 32*t^9 - 32*t^8 - 32*t^7 - 32*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1).
%t A168999 coxG[{23,528,-32}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 11 2021 *)
%Y A168999 Cf. A170753 (G.f.: (1+x)/(1-33*x)).
%K A168999 nonn
%O A168999 0,2
%A A168999 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009