cp's OEIS Frontend

A170016 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

%I A170016 #9 Nov 26 2016 09:38:57
%S A170016 1,7,42,252,1512,9072,54432,326592,1959552,11757312,70543872,
%T A170016 423263232,2539579392,15237476352,91424858112,548549148672,
%U A170016 3291294892032,19747769352192,118486616113152,710919696678912,4265518180073472
%N A170016 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
%C A170016 The initial terms coincide with those of A003949, although the two sequences are eventually different.
%C A170016 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170016 <a href="/index/Rec#order_36">Index entries for linear recurrences with constant coefficients</a>, signature (5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, -15).
%F A170016 G.f. (t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170016 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 +
%F A170016 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 +
%F A170016 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4
%F A170016 + 2*t^3 + 2*t^2 + 2*t + 1)/(15*t^36 - 5*t^35 - 5*t^34 - 5*t^33 - 5*t^32
%F A170016 - 5*t^31 - 5*t^30 - 5*t^29 - 5*t^28 - 5*t^27 - 5*t^26 - 5*t^25 - 5*t^24
%F A170016 - 5*t^23 - 5*t^22 - 5*t^21 - 5*t^20 - 5*t^19 - 5*t^18 - 5*t^17 - 5*t^16
%F A170016 - 5*t^15 - 5*t^14 - 5*t^13 - 5*t^12 - 5*t^11 - 5*t^10 - 5*t^9 - 5*t^8 -
%F A170016 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1)
%t A170016 With[{num=Total[2t^Range[35]]+t^36+1,den=Total[-5 t^Range[35]]+ 15t^36+1}, CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Nov 06 2011 *)
%K A170016 nonn
%O A170016 0,2
%A A170016 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009