cp's OEIS Frontend

A168773 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

%I A168773 #16 Nov 24 2016 14:04:00
%S A168773 1,48,2256,106032,4983504,234224688,11008560336,517402335792,
%T A168773 24317909782224,1142941759764528,53718262708932816,
%U A168773 2524758347319842352,118663642324032590544,5577191189229531755568,262127985893787992511696
%N A168773 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.
%C A168773 The initial terms coincide with those of A170767, although the two sequences are eventually different.
%C A168773 First disagreement at index 18: a(18) = 1279100952334185285087465247848, A170767(18) = 1279100952334185285087465248976. - _Klaus Brockhaus_, Mar 25 2011
%C A168773 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168773 G. C. Greubel, <a href="/A168773/b168773.txt">Table of n, a(n) for n = 0..500</a>
%H A168773 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, -1081).
%F A168773 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)/(1081*t^18 - 46*t^17 - 46*t^16 - 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).
%t A168773 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)/(1081*t^18 - 46*t^17 - 46*t^16 - 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 12 2016 *)
%Y A168773 Cf. A170767 (G.f.: (1+x)/(1-47*x)).
%K A168773 nonn
%O A168773 0,2
%A A168773 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009