cp's OEIS Frontend

A170555 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.

%I A170555 #8 Jul 28 2018 13:45:27
%S A170555 1,18,306,5202,88434,1503378,25557426,434476242,7386096114,
%T A170555 125563633938,2134581776946,36287890208082,616894133537394,
%U A170555 10487200270135698,178282404592306866,3030800878069216722,51523614927176684274
%N A170555 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
%C A170555 The initial terms coincide with those of A170737, although the two sequences are eventually different.
%C A170555 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170555 <a href="/index/Rec#order_47">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, 16, 16, -136).
%F A170555 G.f. (t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 +
%F A170555 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 +
%F A170555 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 +
%F A170555 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 +
%F A170555 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 +
%F A170555 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(136*t^47 -
%F A170555 16*t^46 - 16*t^45 - 16*t^44 - 16*t^43 - 16*t^42 - 16*t^41 - 16*t^40 -
%F A170555 16*t^39 - 16*t^38 - 16*t^37 - 16*t^36 - 16*t^35 - 16*t^34 - 16*t^33 -
%F A170555 16*t^32 - 16*t^31 - 16*t^30 - 16*t^29 - 16*t^28 - 16*t^27 - 16*t^26 -
%F A170555 16*t^25 - 16*t^24 - 16*t^23 - 16*t^22 - 16*t^21 - 16*t^20 - 16*t^19 -
%F A170555 16*t^18 - 16*t^17 - 16*t^16 - 16*t^15 - 16*t^14 - 16*t^13 - 16*t^12 -
%F A170555 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4
%F A170555 - 16*t^3 - 16*t^2 - 16*t + 1)
%t A170555 coxG[{47,136,-16}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 28 2018 *)
%K A170555 nonn
%O A170555 0,2
%A A170555 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009