cp's OEIS Frontend

A170660 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.

%I A170660 #8 Nov 21 2016 11:25:27
%S A170660 1,27,702,18252,474552,12338352,320797152,8340725952,216858874752,
%T A170660 5638330743552,146596599332352,3811511582641152,99099301148669952,
%U A170660 2576581829865418752,66991127576500887552,1741769316989023076352
%N A170660 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
%C A170660 The initial terms coincide with those of A170746, although the two sequences are eventually different.
%C A170660 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170660 <a href="/index/Rec#order_49">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, 25, 25, 25, 25, 25, -325).
%F A170660 G.f. (t^49 + 2*t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 +
%F A170660 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +
%F A170660 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +
%F A170660 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 +
%F A170660 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 +
%F A170660 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170660 1)/(325*t^49 - 25*t^48 - 25*t^47 - 25*t^46 - 25*t^45 - 25*t^44 - 25*t^43
%F A170660 - 25*t^42 - 25*t^41 - 25*t^40 - 25*t^39 - 25*t^38 - 25*t^37 - 25*t^36 -
%F A170660 25*t^35 - 25*t^34 - 25*t^33 - 25*t^32 - 25*t^31 - 25*t^30 - 25*t^29 -
%F A170660 25*t^28 - 25*t^27 - 25*t^26 - 25*t^25 - 25*t^24 - 25*t^23 - 25*t^22 -
%F A170660 25*t^21 - 25*t^20 - 25*t^19 - 25*t^18 - 25*t^17 - 25*t^16 - 25*t^15 -
%F A170660 25*t^14 - 25*t^13 - 25*t^12 - 25*t^11 - 25*t^10 - 25*t^9 - 25*t^8 -
%F A170660 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1)
%t A170660 coxG[{49,325,-25}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 20 2016 *)
%K A170660 nonn
%O A170660 0,2
%A A170660 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009