cp's OEIS Frontend

A170030 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

%I A170030 #9 Nov 26 2016 09:42:54
%S A170030 1,21,420,8400,168000,3360000,67200000,1344000000,26880000000,
%T A170030 537600000000,10752000000000,215040000000000,4300800000000000,
%U A170030 86016000000000000,1720320000000000000,34406400000000000000
%N A170030 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
%C A170030 The initial terms coincide with those of A170740, although the two sequences are eventually different.
%C A170030 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170030 <a href="/index/Rec#order_36">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, 19, 19, -190).
%F A170030 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 A170030 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 A170030 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 A170030 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 A170030 + 2*t^3 + 2*t^2 + 2*t + 1)/(190*t^36 - 19*t^35 - 19*t^34 - 19*t^33 -
%F A170030 19*t^32 - 19*t^31 - 19*t^30 - 19*t^29 - 19*t^28 - 19*t^27 - 19*t^26 -
%F A170030 19*t^25 - 19*t^24 - 19*t^23 - 19*t^22 - 19*t^21 - 19*t^20 - 19*t^19 -
%F A170030 19*t^18 - 19*t^17 - 19*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 -
%F A170030 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4
%F A170030 - 19*t^3 - 19*t^2 - 19*t + 1)
%t A170030 With[{num=Total[2t^Range[35]]+t^36+1,den=Total[-19 t^Range[35]]+ 190t^36+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jan 12 2012 *)
%K A170030 nonn
%O A170030 0,2
%A A170030 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009