cp's OEIS Frontend

A170027 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

%I A170027 #9 Nov 26 2016 09:42:07
%S A170027 1,18,306,5202,88434,1503378,25557426,434476242,7386096114,
%T A170027 125563633938,2134581776946,36287890208082,616894133537394,
%U A170027 10487200270135698,178282404592306866,3030800878069216722,51523614927176684274
%N A170027 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
%C A170027 The initial terms coincide with those of A170737, although the two sequences are eventually different.
%C A170027 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170027 <a href="/index/Rec#order_36">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, -136).
%F A170027 G.f. (t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170027 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 +
%F A170027 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 +
%F A170027 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4
%F A170027 + 2*t^3 + 2*t^2 + 2*t + 1)/(136*t^36 - 16*t^35 - 16*t^34 - 16*t^33 -
%F A170027 16*t^32 - 16*t^31 - 16*t^30 - 16*t^29 - 16*t^28 - 16*t^27 - 16*t^26 -
%F A170027 16*t^25 - 16*t^24 - 16*t^23 - 16*t^22 - 16*t^21 - 16*t^20 - 16*t^19 -
%F A170027 16*t^18 - 16*t^17 - 16*t^16 - 16*t^15 - 16*t^14 - 16*t^13 - 16*t^12 -
%F A170027 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 A170027 - 16*t^3 - 16*t^2 - 16*t + 1)
%t A170027 With[{num=Total[2t^Range[35]]+t^36+1,den=Total[-16 t^Range[35]]+ 136t^36+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Apr 02 2012 *)
%K A170027 nonn
%O A170027 0,2
%A A170027 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009