cp's OEIS Frontend

A168805 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

%I A168805 #12 Nov 24 2016 16:22:56
%S A168805 1,32,992,30752,953312,29552672,916132832,28400117792,880403651552,
%T A168805 27292513198112,846067909141472,26228105183385632,813071260684954592,
%U A168805 25205209081233592352,781361481518241362912,24222205927065482250272
%N A168805 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
%C A168805 The initial terms coincide with those of A170751, although the two sequences are eventually different.
%C A168805 First disagreement at index 19: a(19) = 22369715839969441233253447216, A170751(19) = 22369715839969441233253447712. - _Klaus Brockhaus_, Apr 01 2011
%C A168805 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168805 G. C. Greubel, <a href="/A168805/b168805.txt">Table of n, a(n) for n = 0..500</a>
%H A168805 <a href="/index/Rec#order_19">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, 30, -465).
%F A168805 G.f.: (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)/(465*t^19 - 30*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 A168805 CoefficientList[Series[(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)/(465*t^19 - 30*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 16 2016 *)
%Y A168805 Cf. A170751 (G.f.: (1+x)/(1-31*x)).
%K A168805 nonn
%O A168805 0,2
%A A168805 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009