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A170363 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

%I A170363 #8 Jul 02 2024 14:16:25
%S A170363 1,18,306,5202,88434,1503378,25557426,434476242,7386096114,
%T A170363 125563633938,2134581776946,36287890208082,616894133537394,
%U A170363 10487200270135698,178282404592306866,3030800878069216722,51523614927176684274
%N A170363 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
%C A170363 The initial terms coincide with those of A170737, although the two sequences are eventually different.
%C A170363 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170363 <a href="/index/Rec#order_43">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, -136).
%F A170363 G.f. (t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 +
%F A170363 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A170363 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 A170363 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 A170363 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 A170363 + 2*t^2 + 2*t + 1)/(136*t^43 - 16*t^42 - 16*t^41 - 16*t^40 - 16*t^39 -
%F A170363 16*t^38 - 16*t^37 - 16*t^36 - 16*t^35 - 16*t^34 - 16*t^33 - 16*t^32 -
%F A170363 16*t^31 - 16*t^30 - 16*t^29 - 16*t^28 - 16*t^27 - 16*t^26 - 16*t^25 -
%F A170363 16*t^24 - 16*t^23 - 16*t^22 - 16*t^21 - 16*t^20 - 16*t^19 - 16*t^18 -
%F A170363 16*t^17 - 16*t^16 - 16*t^15 - 16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 -
%F A170363 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 -
%F A170363 16*t^2 - 16*t + 1)
%t A170363 coxG[{43,136,-16}] (* The coxG program is at A169452 *)  (* _Harvey P. Dale_, Jul 02 2024 *)
%K A170363 nonn
%O A170363 0,2
%A A170363 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009