cp's OEIS Frontend

A170084 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.

%I A170084 #8 Aug 09 2025 12:39:08
%S A170084 1,27,702,18252,474552,12338352,320797152,8340725952,216858874752,
%T A170084 5638330743552,146596599332352,3811511582641152,99099301148669952,
%U A170084 2576581829865418752,66991127576500887552,1741769316989023076352
%N A170084 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
%C A170084 The initial terms coincide with those of A170746, although the two sequences are eventually different.
%C A170084 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170084 <a href="/index/Rec#order_37">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, -325).
%F A170084 G.f. (t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 +
%F A170084 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 +
%F A170084 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 +
%F A170084 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 +
%F A170084 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(325*t^37 - 25*t^36 - 25*t^35 -
%F A170084 25*t^34 - 25*t^33 - 25*t^32 - 25*t^31 - 25*t^30 - 25*t^29 - 25*t^28 -
%F A170084 25*t^27 - 25*t^26 - 25*t^25 - 25*t^24 - 25*t^23 - 25*t^22 - 25*t^21 -
%F A170084 25*t^20 - 25*t^19 - 25*t^18 - 25*t^17 - 25*t^16 - 25*t^15 - 25*t^14 -
%F A170084 25*t^13 - 25*t^12 - 25*t^11 - 25*t^10 - 25*t^9 - 25*t^8 - 25*t^7 -
%F A170084 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1)
%t A170084 coxG[{37,325,-25}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 09 2025 *)
%K A170084 nonn
%O A170084 0,2
%A A170084 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009