cp's OEIS Frontend

A168794 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

%I A168794 #12 Nov 24 2016 16:19:35
%S A168794 1,21,420,8400,168000,3360000,67200000,1344000000,26880000000,
%T A168794 537600000000,10752000000000,215040000000000,4300800000000000,
%U A168794 86016000000000000,1720320000000000000,34406400000000000000
%N A168794 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
%C A168794 The initial terms coincide with those of A170740, although the two sequences are eventually different.
%C A168794 First disagreement at index 19: a(19) = 5505023999999999999999790, A170740(19) = 5505024000000000000000000. - _Klaus Brockhaus_, Mar 30 2011
%C A168794 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168794 G. C. Greubel, <a href="/A168794/b168794.txt">Table of n, a(n) for n = 0..500</a>
%H A168794 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).
%F A168794 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)/(190*t^19 - 19*t^18 - 19*t^17 - 19*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).
%t A168794 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)/(190*t^19 - 19*t^18 - 19*t^17 - 19*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 15 2016 *)
%Y A168794 Cf. A170740 (G.f.: (1+x)/(1-20*x)).
%K A168794 nonn
%O A168794 0,2
%A A168794 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009