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A022163 First row of spectral array W(sqrt(3/2)).

%I A022163 #21 May 14 2019 11:11:32
%S A022163 1,5,6,27,33,147,180,801,981,4365,5346,23787,29133,129627,158760,
%T A022163 706401,865161,3849525,4714686,20977947,25692633,114319107,140011740,
%U A022163 622980801,762992541
%N A022163 First row of spectral array W(sqrt(3/2)).
%H A022163 A. Fraenkel and C. Kimberling, <a href="http://dx.doi.org/10.1016/0012-365X(94)90259-3">Generalized Wythoff arrays, shuffles and interspersions</a>, Discrete Mathematics 126 (1994) 137-149.
%F A022163 Conjectures: a(n) = 6*a(n-2)-3*a(n-4). G.f.: -(3*x^3-5*x-1) / (3*x^4-6*x^2+1). - _Colin Barker_, Oct 23 2014
%o A022163 (PARI)
%o A022163 \\ The first row of the generalized Wythoff array W(h),
%o A022163 \\   where h is an irrational number between 1 and 2.
%o A022163 row1(h, m) = {
%o A022163   my(
%o A022163     a=vector(m, n, floor(n*h)),
%o A022163     b=setminus(vector(m, n, n), a),
%o A022163     w=[a[1]^2, b[a[1]]],
%o A022163     j=3
%o A022163   );
%o A022163   while(1,
%o A022163     if(j%2==1,
%o A022163       if(w[j-1]<=#a, w=concat(w, a[w[j-1]]), return(w))
%o A022163     ,
%o A022163       if(w[j-2]<=#b, w=concat(w, b[w[j-2]]), return(w))
%o A022163     );
%o A022163     j++
%o A022163   );
%o A022163   w
%o A022163 }
%o A022163 row1(sqrt(3/2), 100000) \\ _Colin Barker_, Oct 23 2014
%K A022163 nonn,more
%O A022163 0,2
%A A022163 _Clark Kimberling_
%E A022163 a(14)-a(18) from _Colin Barker_, Oct 23 2014 and _Michel Marcus_, Oct 24 2014
%E A022163 a(19)-a(24) from _Sean A. Irvine_, May 13 2019