cp's OEIS Frontend

A169514 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.

%I A169514 #9 Nov 26 2016 07:35:27
%S A169514 1,21,420,8400,168000,3360000,67200000,1344000000,26880000000,
%T A169514 537600000000,10752000000000,215040000000000,4300800000000000,
%U A169514 86016000000000000,1720320000000000000,34406400000000000000
%N A169514 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
%C A169514 The initial terms coincide with those of A170740, although the two sequences are eventually different.
%C A169514 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169514 <a href="/index/Rec#order_34">Index entries for linear recurrences with constant coefficients</a>, signature (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).
%F A169514 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 A169514 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 A169514 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 A169514 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 A169514 2*t + 1)/(190*t^34 - 19*t^33 - 19*t^32 - 19*t^31 - 19*t^30 - 19*t^29 -
%F A169514 19*t^28 - 19*t^27 - 19*t^26 - 19*t^25 - 19*t^24 - 19*t^23 - 19*t^22 -
%F A169514 19*t^21 - 19*t^20 - 19*t^19 - 19*t^18 - 19*t^17 - 19*t^16 - 19*t^15 -
%F A169514 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 -
%F A169514 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1)
%t A169514 With[{num=Total[2t^Range[33]]+t^34+1,den=Total[-19 t^Range[33]]+ 190t^34+ 1}, CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Nov 25 2011 *)
%K A169514 nonn
%O A169514 0,2
%A A169514 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009