cp's OEIS Frontend

A169171 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.

%I A169171 #8 Nov 25 2016 13:56:32
%S A169171 1,14,182,2366,30758,399854,5198102,67575326,878479238,11420230094,
%T A169171 148462991222,1930018885886,25090245516518,326173191714734,
%U A169171 4240251492291542,55123269399790046,716602502197270598
%N A169171 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
%C A169171 The initial terms coincide with those of A170733, although the two sequences are eventually different.
%C A169171 First disagreement at index 27: a(27) = 1284266622705760633217594624035, A170733(27) = 1284266622705760633217594624126. - Klaus Brockhaus, May 07 2011
%C A169171 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169171 <a href="/index/Rec#order_27">Index entries for linear recurrences with constant coefficients</a>, signature (12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, -78).
%F A169171 G.f.: (t^27 + 2*t^26 + 2*t^25 + 2*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)/(78*t^27 - 12*t^26 - 12*t^25 - 12*t^24 - 12*t^23 - 12*t^22 - 12*t^21 - 12*t^20 - 12*t^19 - 12*t^18 - 12*t^17 - 12*t^16 - 12*t^15 - 12*t^14 - 12*t^13 - 12*t^12 - 12*t^11 - 12*t^10 - 12*t^9 - 12*t^8 - 12*t^7 - 12*t^6 - 12*t^5 - 12*t^4 - 12*t^3 - 12*t^2 - 12*t + 1).
%Y A169171 Cf. A170733 (G.f.: (1+x)/(1-13*x)).
%K A169171 nonn
%O A169171 0,2
%A A169171 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009