cp's OEIS Frontend

A169500 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.

%I A169500 #8 Nov 26 2016 07:31:29
%S A169500 1,7,42,252,1512,9072,54432,326592,1959552,11757312,70543872,
%T A169500 423263232,2539579392,15237476352,91424858112,548549148672,
%U A169500 3291294892032,19747769352192,118486616113152,710919696678912,4265518180073472
%N A169500 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
%C A169500 The initial terms coincide with those of A003949, although the two sequences are eventually different.
%C A169500 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169500 <a href="/index/Rec#order_34">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, -15).
%F A169500 G.f. (t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A169500 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A169500 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A169500 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 +
%F A169500 2*t + 1)/(15*t^34 - 5*t^33 - 5*t^32 - 5*t^31 - 5*t^30 - 5*t^29 - 5*t^28
%F A169500 - 5*t^27 - 5*t^26 - 5*t^25 - 5*t^24 - 5*t^23 - 5*t^22 - 5*t^21 - 5*t^20
%F A169500 - 5*t^19 - 5*t^18 - 5*t^17 - 5*t^16 - 5*t^15 - 5*t^14 - 5*t^13 - 5*t^12
%F A169500 - 5*t^11 - 5*t^10 - 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 -
%F A169500 5*t^3 - 5*t^2 - 5*t + 1)
%t A169500 With[{num=Total[2t^Range[33]]+t^34+1,den=Total[-5 t^Range[33]]+ 15t^34+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Mar 27 2013 *)
%K A169500 nonn
%O A169500 0,2
%A A169500 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009