cp's OEIS Frontend

A170447 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.

%I A170447 #8 Jan 30 2019 17:01:19
%S A170447 1,6,30,150,750,3750,18750,93750,468750,2343750,11718750,58593750,
%T A170447 292968750,1464843750,7324218750,36621093750,183105468750,
%U A170447 915527343750,4577636718750,22888183593750,114440917968750,572204589843750
%N A170447 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
%C A170447 The initial terms coincide with those of A003948, although the two sequences are eventually different.
%C A170447 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170447 <a href="/index/Rec#order_45">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, 4, 4, 4, 4, -10).
%F A170447 G.f. (t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 +
%F A170447 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 +
%F A170447 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 A170447 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 A170447 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 A170447 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(10*t^45 - 4*t^44 - 4*t^43 -
%F A170447 4*t^42 - 4*t^41 - 4*t^40 - 4*t^39 - 4*t^38 - 4*t^37 - 4*t^36 - 4*t^35 -
%F A170447 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 A170447 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 A170447 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 A170447 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 A170447 4*t + 1)
%t A170447 coxG[{45,10,-4,30}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 30 2019 *)
%K A170447 nonn
%O A170447 0,2
%A A170447 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009