cp's OEIS Frontend

A170564 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.

%I A170564 #8 May 28 2017 09:52:00
%S A170564 1,27,702,18252,474552,12338352,320797152,8340725952,216858874752,
%T A170564 5638330743552,146596599332352,3811511582641152,99099301148669952,
%U A170564 2576581829865418752,66991127576500887552,1741769316989023076352
%N A170564 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
%C A170564 The initial terms coincide with those of A170746, although the two sequences are eventually different.
%C A170564 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170564 <a href="/index/Rec#order_47">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, -325).
%F A170564 G.f. (t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 +
%F A170564 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 +
%F A170564 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 +
%F A170564 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 +
%F A170564 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 +
%F A170564 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(325*t^47 -
%F A170564 25*t^46 - 25*t^45 - 25*t^44 - 25*t^43 - 25*t^42 - 25*t^41 - 25*t^40 -
%F A170564 25*t^39 - 25*t^38 - 25*t^37 - 25*t^36 - 25*t^35 - 25*t^34 - 25*t^33 -
%F A170564 25*t^32 - 25*t^31 - 25*t^30 - 25*t^29 - 25*t^28 - 25*t^27 - 25*t^26 -
%F A170564 25*t^25 - 25*t^24 - 25*t^23 - 25*t^22 - 25*t^21 - 25*t^20 - 25*t^19 -
%F A170564 25*t^18 - 25*t^17 - 25*t^16 - 25*t^15 - 25*t^14 - 25*t^13 - 25*t^12 -
%F A170564 25*t^11 - 25*t^10 - 25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4
%F A170564 - 25*t^3 - 25*t^2 - 25*t + 1)
%t A170564 coxG[{47,325,-25}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 28 2017 *)
%K A170564 nonn
%O A170564 0,2
%A A170564 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009