cp's OEIS Frontend

A169527 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.

%I A169527 #8 Apr 25 2020 18:26:39
%S A169527 1,34,1122,37026,1221858,40321314,1330603362,43909910946,
%T A169527 1449027061218,47817893020194,1577990469666402,52073685498991266,
%U A169527 1718431621466711778,56708243508401488674,1871372035777249126242,61755277180649221165986
%N A169527 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
%C A169527 The initial terms coincide with those of A170753, although the two sequences are eventually different.
%C A169527 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169527 <a href="/index/Rec#order_34">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, -528).
%F A169527 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 A169527 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 A169527 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 A169527 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 A169527 2*t + 1)/(528*t^34 - 32*t^33 - 32*t^32 - 32*t^31 - 32*t^30 - 32*t^29 -
%F A169527 32*t^28 - 32*t^27 - 32*t^26 - 32*t^25 - 32*t^24 - 32*t^23 - 32*t^22 -
%F A169527 32*t^21 - 32*t^20 - 32*t^19 - 32*t^18 - 32*t^17 - 32*t^16 - 32*t^15 -
%F A169527 32*t^14 - 32*t^13 - 32*t^12 - 32*t^11 - 32*t^10 - 32*t^9 - 32*t^8 -
%F A169527 32*t^7 - 32*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1)
%t A169527 coxG[{34,528,-32}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 25 2020 *)
%K A169527 nonn
%O A169527 0,2
%A A169527 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009