cp's OEIS Frontend

A170075 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.

%I A170075 #6 Nov 26 2016 10:02:34
%S A170075 1,18,306,5202,88434,1503378,25557426,434476242,7386096114,
%T A170075 125563633938,2134581776946,36287890208082,616894133537394,
%U A170075 10487200270135698,178282404592306866,3030800878069216722,51523614927176684274
%N A170075 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
%C A170075 The initial terms coincide with those of A170737, although the two sequences are eventually different.
%C A170075 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170075 <a href="/index/Rec#order_37">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, -136).
%F A170075 G.f. (t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 +
%F A170075 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 A170075 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 A170075 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 A170075 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(136*t^37 - 16*t^36 - 16*t^35 -
%F A170075 16*t^34 - 16*t^33 - 16*t^32 - 16*t^31 - 16*t^30 - 16*t^29 - 16*t^28 -
%F A170075 16*t^27 - 16*t^26 - 16*t^25 - 16*t^24 - 16*t^23 - 16*t^22 - 16*t^21 -
%F A170075 16*t^20 - 16*t^19 - 16*t^18 - 16*t^17 - 16*t^16 - 16*t^15 - 16*t^14 -
%F A170075 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 -
%F A170075 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1)
%K A170075 nonn
%O A170075 0,2
%A A170075 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009