cp's OEIS Frontend

A170420 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.

%I A170420 #6 Nov 21 2016 17:28:35
%S A170420 1,27,702,18252,474552,12338352,320797152,8340725952,216858874752,
%T A170420 5638330743552,146596599332352,3811511582641152,99099301148669952,
%U A170420 2576581829865418752,66991127576500887552,1741769316989023076352
%N A170420 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
%C A170420 The initial terms coincide with those of A170746, although the two sequences are eventually different.
%C A170420 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170420 <a href="/index/Rec#order_44">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, 25, -325).
%F A170420 G.f. (t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 +
%F A170420 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170420 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 +
%F A170420 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 +
%F A170420 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
%F A170420 + 2*t^3 + 2*t^2 + 2*t + 1)/(325*t^44 - 25*t^43 - 25*t^42 - 25*t^41 -
%F A170420 25*t^40 - 25*t^39 - 25*t^38 - 25*t^37 - 25*t^36 - 25*t^35 - 25*t^34 -
%F A170420 25*t^33 - 25*t^32 - 25*t^31 - 25*t^30 - 25*t^29 - 25*t^28 - 25*t^27 -
%F A170420 25*t^26 - 25*t^25 - 25*t^24 - 25*t^23 - 25*t^22 - 25*t^21 - 25*t^20 -
%F A170420 25*t^19 - 25*t^18 - 25*t^17 - 25*t^16 - 25*t^15 - 25*t^14 - 25*t^13 -
%F A170420 25*t^12 - 25*t^11 - 25*t^10 - 25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5
%F A170420 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1)
%K A170420 nonn
%O A170420 0,2
%A A170420 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009