cp's OEIS Frontend

A169431 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169431 #13 Jun 13 2020 10:48:50
%S A169431 1,34,1122,37026,1221858,40321314,1330603362,43909910946,
%T A169431 1449027061218,47817893020194,1577990469666402,52073685498991266,
%U A169431 1718431621466711778,56708243508401488674,1871372035777249126242,61755277180649221165986
%N A169431 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169431 The initial terms coincide with those of A170753, although the two sequences are eventually different.
%C A169431 First disagreement is at index 32, the difference is 561. - _Klaus Brockhaus_, Jun 30 2011
%C A169431 Computed with Magma using commands similar to those used to compute A154638.
%H A169431 <a href="/index/Rec#order_32">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, -528).
%F A169431 G.f.: (t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 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 + 2*t^3 + 2*t^2 + 2*t + 1)/(528*t^32 - 32*t^31 - 32*t^30 - 32*t^29 - 32*t^28 - 32*t^27 - 32*t^26 - 32*t^25 - 32*t^24 - 32*t^23 - 32*t^22 - 32*t^21 - 32*t^20 - 32*t^19 - 32*t^18 - 32*t^17 - 32*t^16 - 32*t^15 - 32*t^14 - 32*t^13 - 32*t^12 - 32*t^11 - 32*t^10 - 32*t^9 - 32*t^8 - 32*t^7 - 32*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1).
%F A169431 G.f.: (1+2*sum(k=1..31,x^k)+x^32)/(1-32*sum(k=1..31,x^k)+528*x^32).
%t A169431 coxG[{32,528,-32}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 13 2020 *)
%Y A169431 Cf. A170753 (G.f.: (1+x)/(1-33*x) ).
%K A169431 nonn
%O A169431 0,2
%A A169431 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009