cp's OEIS Frontend

A168757 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

%I A168757 #14 Nov 24 2016 13:59:10
%S A168757 1,32,992,30752,953312,29552672,916132832,28400117792,880403651552,
%T A168757 27292513198112,846067909141472,26228105183385632,813071260684954592,
%U A168757 25205209081233592352,781361481518241362912,24222205927065482250272
%N A168757 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.
%C A168757 The initial terms coincide with those of A170751, although the two sequences are eventually different.
%C A168757 First disagreement at index 18: a(18) = 721603736773207781717852656, A170751(18) = 721603736773207781717853152. - _Klaus Brockhaus_, Mar 26 2011
%C A168757 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168757 G. C. Greubel, <a href="/A168757/b168757.txt">Table of n, a(n) for n = 0..500</a>
%H A168757 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, -465).
%F A168757 G.f.: (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)/(465*t^18 - 30*t^17 - 30*t^16 - 30*t^15 - 30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).
%t A168757 CoefficientList[Series[(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)/(465*t^18 - 30*t^17 - 30*t^16 - 30*t^15 - 30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 11 2016 *)
%Y A168757 Cf. A170751 (G.f.: (1+x)/(1-31*x)).
%K A168757 nonn,easy
%O A168757 0,2
%A A168757 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009