cp's OEIS Frontend

A170053 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

%I A170053 #8 Nov 26 2016 09:49:07
%S A170053 1,44,1892,81356,3498308,150427244,6468371492,278139974156,
%T A170053 11960018888708,514280812214444,22114074925221092,950905221784506956,
%U A170053 40888924536733799108,1758223755079553361644,75603621468420794550692
%N A170053 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
%C A170053 The initial terms coincide with those of A170763, although the two sequences are eventually different.
%C A170053 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170053 <a href="/index/Rec#order_36">Index entries for linear recurrences with constant coefficients</a>, signature (42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, -903).
%F A170053 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 A170053 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 A170053 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 A170053 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 A170053 + 2*t^3 + 2*t^2 + 2*t + 1)/(903*t^36 - 42*t^35 - 42*t^34 - 42*t^33 -
%F A170053 42*t^32 - 42*t^31 - 42*t^30 - 42*t^29 - 42*t^28 - 42*t^27 - 42*t^26 -
%F A170053 42*t^25 - 42*t^24 - 42*t^23 - 42*t^22 - 42*t^21 - 42*t^20 - 42*t^19 -
%F A170053 42*t^18 - 42*t^17 - 42*t^16 - 42*t^15 - 42*t^14 - 42*t^13 - 42*t^12 -
%F A170053 42*t^11 - 42*t^10 - 42*t^9 - 42*t^8 - 42*t^7 - 42*t^6 - 42*t^5 - 42*t^4
%F A170053 - 42*t^3 - 42*t^2 - 42*t + 1)
%t A170053 With[{num=Total[2t^Range[35]]+t^36+1,den=Total[-42 t^Range[35]]+903t^36+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Apr 22 2013 *)
%K A170053 nonn
%O A170053 0,2
%A A170053 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009