cp's OEIS Frontend

A170372 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

%I A170372 #6 Nov 21 2016 19:26:23
%S A170372 1,27,702,18252,474552,12338352,320797152,8340725952,216858874752,
%T A170372 5638330743552,146596599332352,3811511582641152,99099301148669952,
%U A170372 2576581829865418752,66991127576500887552,1741769316989023076352
%N A170372 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
%C A170372 The initial terms coincide with those of A170746, although the two sequences are eventually different.
%C A170372 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170372 <a href="/index/Rec#order_43">Index entries for linear recurrences with constant coefficients</a>, signature (25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, -325).
%F A170372 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 A170372 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 A170372 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 A170372 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 A170372 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 A170372 + 2*t^2 + 2*t + 1)/(325*t^43 - 25*t^42 - 25*t^41 - 25*t^40 - 25*t^39 -
%F A170372 25*t^38 - 25*t^37 - 25*t^36 - 25*t^35 - 25*t^34 - 25*t^33 - 25*t^32 -
%F A170372 25*t^31 - 25*t^30 - 25*t^29 - 25*t^28 - 25*t^27 - 25*t^26 - 25*t^25 -
%F A170372 25*t^24 - 25*t^23 - 25*t^22 - 25*t^21 - 25*t^20 - 25*t^19 - 25*t^18 -
%F A170372 25*t^17 - 25*t^16 - 25*t^15 - 25*t^14 - 25*t^13 - 25*t^12 - 25*t^11 -
%F A170372 25*t^10 - 25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 -
%F A170372 25*t^2 - 25*t + 1)
%K A170372 nonn
%O A170372 0,2
%A A170372 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009