cp's OEIS Frontend

A169559 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

%I A169559 #8 Jun 03 2020 14:21:26
%S A169559 1,18,306,5202,88434,1503378,25557426,434476242,7386096114,
%T A169559 125563633938,2134581776946,36287890208082,616894133537394,
%U A169559 10487200270135698,178282404592306866,3030800878069216722,51523614927176684274
%N A169559 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
%C A169559 The initial terms coincide with those of A170737, although the two sequences are eventually different.
%C A169559 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169559 <a href="/index/Rec#order_35">Index entries for linear recurrences with constant coefficients</a>, signature (16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, -136).
%F A169559 G.f. (t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A169559 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 +
%F A169559 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 +
%F A169559 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
%F A169559 + 2*t^2 + 2*t + 1)/(136*t^35 - 16*t^34 - 16*t^33 - 16*t^32 - 16*t^31 -
%F A169559 16*t^30 - 16*t^29 - 16*t^28 - 16*t^27 - 16*t^26 - 16*t^25 - 16*t^24 -
%F A169559 16*t^23 - 16*t^22 - 16*t^21 - 16*t^20 - 16*t^19 - 16*t^18 - 16*t^17 -
%F A169559 16*t^16 - 16*t^15 - 16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 -
%F A169559 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 -
%F A169559 16*t + 1)
%t A169559 coxG[{35,136,-16}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 03 2020 *)
%K A169559 nonn
%O A169559 0,2
%A A169559 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009