cp's OEIS Frontend

A170228 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.

%I A170228 #8 Aug 10 2021 18:24:22
%S A170228 1,27,702,18252,474552,12338352,320797152,8340725952,216858874752,
%T A170228 5638330743552,146596599332352,3811511582641152,99099301148669952,
%U A170228 2576581829865418752,66991127576500887552,1741769316989023076352
%N A170228 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
%C A170228 The initial terms coincide with those of A170746, although the two sequences are eventually different.
%C A170228 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170228 <a href="/index/Rec#order_40">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, -325).
%F A170228 G.f. (t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 +
%F A170228 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 +
%F A170228 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 +
%F A170228 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 +
%F A170228 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170228 1)/(325*t^40 - 25*t^39 - 25*t^38 - 25*t^37 - 25*t^36 - 25*t^35 - 25*t^34
%F A170228 - 25*t^33 - 25*t^32 - 25*t^31 - 25*t^30 - 25*t^29 - 25*t^28 - 25*t^27 -
%F A170228 25*t^26 - 25*t^25 - 25*t^24 - 25*t^23 - 25*t^22 - 25*t^21 - 25*t^20 -
%F A170228 25*t^19 - 25*t^18 - 25*t^17 - 25*t^16 - 25*t^15 - 25*t^14 - 25*t^13 -
%F A170228 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 A170228 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1)
%t A170228 coxG[{40,325,-25}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 10 2021 *)
%K A170228 nonn
%O A170228 0,2
%A A170228 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009