cp's OEIS Frontend

A170043 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

%I A170043 #8 Oct 01 2017 17:21:14
%S A170043 1,34,1122,37026,1221858,40321314,1330603362,43909910946,
%T A170043 1449027061218,47817893020194,1577990469666402,52073685498991266,
%U A170043 1718431621466711778,56708243508401488674,1871372035777249126242,61755277180649221165986
%N A170043 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
%C A170043 The initial terms coincide with those of A170753, although the two sequences are eventually different.
%C A170043 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170043 <a href="/index/Rec#order_36">Index entries for linear recurrences with constant coefficients</a>, signature (32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, -528).
%F A170043 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 A170043 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 A170043 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 A170043 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 A170043 + 2*t^3 + 2*t^2 + 2*t + 1)/(528*t^36 - 32*t^35 - 32*t^34 - 32*t^33 -
%F A170043 32*t^32 - 32*t^31 - 32*t^30 - 32*t^29 - 32*t^28 - 32*t^27 - 32*t^26 -
%F A170043 32*t^25 - 32*t^24 - 32*t^23 - 32*t^22 - 32*t^21 - 32*t^20 - 32*t^19 -
%F A170043 32*t^18 - 32*t^17 - 32*t^16 - 32*t^15 - 32*t^14 - 32*t^13 - 32*t^12 -
%F A170043 32*t^11 - 32*t^10 - 32*t^9 - 32*t^8 - 32*t^7 - 32*t^6 - 32*t^5 - 32*t^4
%F A170043 - 32*t^3 - 32*t^2 - 32*t + 1)
%t A170043 coxG[{36,528,-32}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 01 2017 *)
%K A170043 nonn
%O A170043 0,2
%A A170043 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009