cp's OEIS Frontend

A169029 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.

%I A169029 #8 Nov 25 2016 10:59:19
%S A169029 1,16,240,3600,54000,810000,12150000,182250000,2733750000,41006250000,
%T A169029 615093750000,9226406250000,138396093750000,2075941406250000,
%U A169029 31139121093750000,467086816406250000,7006302246093750000
%N A169029 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
%C A169029 The initial terms coincide with those of A170735, although the two sequences are eventually different.
%C A169029 First disagreement at index 24: a(24) = 17956386342430114746093749880, A170735(24) = 17956386342430114746093750000. - Klaus Brockhaus, Apr 20 2011
%C A169029 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169029 <a href="/index/Rec#order_24">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, -105).
%F A169029 G.f.: (t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 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 + 2*t^3 + 2*t^2 + 2*t + 1)/(105*t^24 - 14*t^23 - 14*t^22 - 14*t^21 - 14*t^20 - 14*t^19 - 14*t^18 - 14*t^17 - 14*t^16 - 14*t^15 - 14*t^14 - 14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1).
%Y A169029 Cf. A170735 (G.f.: (1+x)/(1-15*x)).
%K A169029 nonn
%O A169029 0,2
%A A169029 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009