cp's OEIS Frontend

A170219 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.

%I A170219 #8 Mar 25 2025 11:14:32
%S A170219 1,18,306,5202,88434,1503378,25557426,434476242,7386096114,
%T A170219 125563633938,2134581776946,36287890208082,616894133537394,
%U A170219 10487200270135698,178282404592306866,3030800878069216722,51523614927176684274
%N A170219 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
%C A170219 The initial terms coincide with those of A170737, although the two sequences are eventually different.
%C A170219 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170219 <a href="/index/Rec#order_40">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, 16, 16, 16, 16, 16, -136).
%F A170219 G.f. (t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 +
%F A170219 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 +
%F A170219 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 +
%F A170219 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 +
%F A170219 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170219 1)/(136*t^40 - 16*t^39 - 16*t^38 - 16*t^37 - 16*t^36 - 16*t^35 - 16*t^34
%F A170219 - 16*t^33 - 16*t^32 - 16*t^31 - 16*t^30 - 16*t^29 - 16*t^28 - 16*t^27 -
%F A170219 16*t^26 - 16*t^25 - 16*t^24 - 16*t^23 - 16*t^22 - 16*t^21 - 16*t^20 -
%F A170219 16*t^19 - 16*t^18 - 16*t^17 - 16*t^16 - 16*t^15 - 16*t^14 - 16*t^13 -
%F A170219 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5
%F A170219 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1)
%t A170219 coxG[{40,136,-16}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Mar 25 2025 *)
%K A170219 nonn
%O A170219 0,2
%A A170219 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009