cp's OEIS Frontend

A170324 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

%I A170324 #6 Nov 22 2016 08:15:40
%S A170324 1,27,702,18252,474552,12338352,320797152,8340725952,216858874752,
%T A170324 5638330743552,146596599332352,3811511582641152,99099301148669952,
%U A170324 2576581829865418752,66991127576500887552,1741769316989023076352
%N A170324 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
%C A170324 The initial terms coincide with those of A170746, although the two sequences are eventually different.
%C A170324 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170324 <a href="/index/Rec#order_42">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, -325).
%F A170324 G.f. (t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +
%F A170324 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A170324 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A170324 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A170324 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 +
%F A170324 2*t + 1)/(325*t^42 - 25*t^41 - 25*t^40 - 25*t^39 - 25*t^38 - 25*t^37 -
%F A170324 25*t^36 - 25*t^35 - 25*t^34 - 25*t^33 - 25*t^32 - 25*t^31 - 25*t^30 -
%F A170324 25*t^29 - 25*t^28 - 25*t^27 - 25*t^26 - 25*t^25 - 25*t^24 - 25*t^23 -
%F A170324 25*t^22 - 25*t^21 - 25*t^20 - 25*t^19 - 25*t^18 - 25*t^17 - 25*t^16 -
%F A170324 25*t^15 - 25*t^14 - 25*t^13 - 25*t^12 - 25*t^11 - 25*t^10 - 25*t^9 -
%F A170324 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1)
%K A170324 nonn
%O A170324 0,2
%A A170324 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009