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A170459 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.

%I A170459 #8 Nov 21 2016 16:51:15
%S A170459 1,18,306,5202,88434,1503378,25557426,434476242,7386096114,
%T A170459 125563633938,2134581776946,36287890208082,616894133537394,
%U A170459 10487200270135698,178282404592306866,3030800878069216722,51523614927176684274
%N A170459 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
%C A170459 The initial terms coincide with those of A170737, although the two sequences are eventually different.
%C A170459 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170459 <a href="/index/Rec#order_45">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, 16, 16, 16, -136).
%F A170459 G.f. (t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 +
%F A170459 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 +
%F A170459 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 +
%F A170459 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 +
%F A170459 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 +
%F A170459 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(136*t^45 - 16*t^44 - 16*t^43 -
%F A170459 16*t^42 - 16*t^41 - 16*t^40 - 16*t^39 - 16*t^38 - 16*t^37 - 16*t^36 -
%F A170459 16*t^35 - 16*t^34 - 16*t^33 - 16*t^32 - 16*t^31 - 16*t^30 - 16*t^29 -
%F A170459 16*t^28 - 16*t^27 - 16*t^26 - 16*t^25 - 16*t^24 - 16*t^23 - 16*t^22 -
%F A170459 16*t^21 - 16*t^20 - 16*t^19 - 16*t^18 - 16*t^17 - 16*t^16 - 16*t^15 -
%F A170459 16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 -
%F A170459 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1)
%t A170459 coxG[{45,136,-16}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 01 2016 *)
%K A170459 nonn
%O A170459 0,2
%A A170459 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009