cp's OEIS Frontend

A170315 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

%I A170315 #6 Nov 22 2016 08:09:50
%S A170315 1,18,306,5202,88434,1503378,25557426,434476242,7386096114,
%T A170315 125563633938,2134581776946,36287890208082,616894133537394,
%U A170315 10487200270135698,178282404592306866,3030800878069216722,51523614927176684274
%N A170315 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
%C A170315 The initial terms coincide with those of A170737, although the two sequences are eventually different.
%C A170315 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170315 <a href="/index/Rec#order_42">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, 16, -136).
%F A170315 G.f. (t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +
%F A170315 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A170315 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A170315 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A170315 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 +
%F A170315 2*t + 1)/(136*t^42 - 16*t^41 - 16*t^40 - 16*t^39 - 16*t^38 - 16*t^37 -
%F A170315 16*t^36 - 16*t^35 - 16*t^34 - 16*t^33 - 16*t^32 - 16*t^31 - 16*t^30 -
%F A170315 16*t^29 - 16*t^28 - 16*t^27 - 16*t^26 - 16*t^25 - 16*t^24 - 16*t^23 -
%F A170315 16*t^22 - 16*t^21 - 16*t^20 - 16*t^19 - 16*t^18 - 16*t^17 - 16*t^16 -
%F A170315 16*t^15 - 16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 -
%F A170315 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1)
%K A170315 nonn
%O A170315 0,2
%A A170315 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009