cp's OEIS Frontend

A169520 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.

%I A169520 #8 Oct 29 2020 19:06:27
%S A169520 1,27,702,18252,474552,12338352,320797152,8340725952,216858874752,
%T A169520 5638330743552,146596599332352,3811511582641152,99099301148669952,
%U A169520 2576581829865418752,66991127576500887552,1741769316989023076352
%N A169520 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
%C A169520 The initial terms coincide with those of A170746, although the two sequences are eventually different.
%C A169520 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169520 <a href="/index/Rec#order_34">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, -325).
%F A169520 G.f. (t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A169520 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 A169520 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 A169520 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 A169520 2*t + 1)/(325*t^34 - 25*t^33 - 25*t^32 - 25*t^31 - 25*t^30 - 25*t^29 -
%F A169520 25*t^28 - 25*t^27 - 25*t^26 - 25*t^25 - 25*t^24 - 25*t^23 - 25*t^22 -
%F A169520 25*t^21 - 25*t^20 - 25*t^19 - 25*t^18 - 25*t^17 - 25*t^16 - 25*t^15 -
%F A169520 25*t^14 - 25*t^13 - 25*t^12 - 25*t^11 - 25*t^10 - 25*t^9 - 25*t^8 -
%F A169520 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1)
%t A169520 coxG[{34,325,-25}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 29 2020 *)
%K A169520 nonn
%O A169520 0,2
%A A169520 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009