cp's OEIS Frontend

A170361 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

%I A170361 #8 Nov 21 2016 19:18:32
%S A170361 1,16,240,3600,54000,810000,12150000,182250000,2733750000,41006250000,
%T A170361 615093750000,9226406250000,138396093750000,2075941406250000,
%U A170361 31139121093750000,467086816406250000,7006302246093750000
%N A170361 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
%C A170361 The initial terms coincide with those of A170735, although the two sequences are eventually different.
%C A170361 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170361 <a href="/index/Rec#order_43">Index entries for linear recurrences with constant coefficients</a>, signature (14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, -105).
%F A170361 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 A170361 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 A170361 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 A170361 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 A170361 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 A170361 + 2*t^2 + 2*t + 1)/(105*t^43 - 14*t^42 - 14*t^41 - 14*t^40 - 14*t^39 -
%F A170361 14*t^38 - 14*t^37 - 14*t^36 - 14*t^35 - 14*t^34 - 14*t^33 - 14*t^32 -
%F A170361 14*t^31 - 14*t^30 - 14*t^29 - 14*t^28 - 14*t^27 - 14*t^26 - 14*t^25 -
%F A170361 14*t^24 - 14*t^23 - 14*t^22 - 14*t^21 - 14*t^20 - 14*t^19 - 14*t^18 -
%F A170361 14*t^17 - 14*t^16 - 14*t^15 - 14*t^14 - 14*t^13 - 14*t^12 - 14*t^11 -
%F A170361 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 -
%F A170361 14*t^2 - 14*t + 1)
%t A170361 With[{num=Total[2t^Range[42]]+t^43+1,den=Total[-14 t^Range[42]]+105t^43+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Oct 14 2013 *)
%K A170361 nonn
%O A170361 0,2
%A A170361 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009