cp's OEIS Frontend

A170267 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.

%I A170267 #8 Nov 22 2016 11:46:24
%S A170267 1,18,306,5202,88434,1503378,25557426,434476242,7386096114,
%T A170267 125563633938,2134581776946,36287890208082,616894133537394,
%U A170267 10487200270135698,178282404592306866,3030800878069216722,51523614927176684274
%N A170267 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
%C A170267 The initial terms coincide with those of A170737, although the two sequences are eventually different.
%C A170267 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170267 <a href="/index/Rec#order_41">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, 16, -136).
%F A170267 G.f. (t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +
%F A170267 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +
%F A170267 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 +
%F A170267 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 +
%F A170267 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 +
%F A170267 1)/(136*t^41 - 16*t^40 - 16*t^39 - 16*t^38 - 16*t^37 - 16*t^36 - 16*t^35
%F A170267 - 16*t^34 - 16*t^33 - 16*t^32 - 16*t^31 - 16*t^30 - 16*t^29 - 16*t^28 -
%F A170267 16*t^27 - 16*t^26 - 16*t^25 - 16*t^24 - 16*t^23 - 16*t^22 - 16*t^21 -
%F A170267 16*t^20 - 16*t^19 - 16*t^18 - 16*t^17 - 16*t^16 - 16*t^15 - 16*t^14 -
%F A170267 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 -
%F A170267 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1)
%t A170267 coxG[{41,136,-16}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 08 2016 *)
%K A170267 nonn
%O A170267 0,2
%A A170267 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009