cp's OEIS Frontend

A170255 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.

%I A170255 #8 Aug 14 2023 16:07:05
%S A170255 1,6,30,150,750,3750,18750,93750,468750,2343750,11718750,58593750,
%T A170255 292968750,1464843750,7324218750,36621093750,183105468750,
%U A170255 915527343750,4577636718750,22888183593750,114440917968750,572204589843750
%N A170255 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
%C A170255 The initial terms coincide with those of A003948, although the two sequences are eventually different.
%C A170255 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170255 <a href="/index/Rec#order_41">Index entries for linear recurrences with constant coefficients</a>, signature (4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -10).
%F A170255 G.f. (t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +
%F A170255 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 A170255 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 A170255 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 A170255 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 A170255 1)/(10*t^41 - 4*t^40 - 4*t^39 - 4*t^38 - 4*t^37 - 4*t^36 - 4*t^35 -
%F A170255 4*t^34 - 4*t^33 - 4*t^32 - 4*t^31 - 4*t^30 - 4*t^29 - 4*t^28 - 4*t^27 -
%F A170255 4*t^26 - 4*t^25 - 4*t^24 - 4*t^23 - 4*t^22 - 4*t^21 - 4*t^20 - 4*t^19 -
%F A170255 4*t^18 - 4*t^17 - 4*t^16 - 4*t^15 - 4*t^14 - 4*t^13 - 4*t^12 - 4*t^11 -
%F A170255 4*t^10 - 4*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 -
%F A170255 4*t + 1)
%t A170255 coxG[{41,10,-4,30}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 14 2023 *)
%K A170255 nonn
%O A170255 0,2
%A A170255 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009