cp's OEIS Frontend

A170207 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.

%I A170207 #11 Sep 20 2024 17:10:42
%S A170207 1,6,30,150,750,3750,18750,93750,468750,2343750,11718750,58593750,
%T A170207 292968750,1464843750,7324218750,36621093750,183105468750,
%U A170207 915527343750,4577636718750,22888183593750,114440917968750,572204589843750
%N A170207 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
%C A170207 The initial terms coincide with those of A003948, although the two sequences are eventually different.
%C A170207 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170207 <a href="/index/Rec#order_40">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, -10).
%F A170207 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 A170207 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 A170207 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 A170207 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 A170207 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170207 1)/(10*t^40 - 4*t^39 - 4*t^38 - 4*t^37 - 4*t^36 - 4*t^35 - 4*t^34 -
%F A170207 4*t^33 - 4*t^32 - 4*t^31 - 4*t^30 - 4*t^29 - 4*t^28 - 4*t^27 - 4*t^26 -
%F A170207 4*t^25 - 4*t^24 - 4*t^23 - 4*t^22 - 4*t^21 - 4*t^20 - 4*t^19 - 4*t^18 -
%F A170207 4*t^17 - 4*t^16 - 4*t^15 - 4*t^14 - 4*t^13 - 4*t^12 - 4*t^11 - 4*t^10 -
%F A170207 4*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t + 1).
%t A170207 coxG[{40,10,-4,30}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 20 2024 *)
%Y A170207 Cf. A003948.
%K A170207 nonn
%O A170207 0,2
%A A170207 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009