A022165 - OEIS

%I #22 May 14 2019 11:11:44

%S 1,5,6,26,32,136,168,712,880,3728,4608,19520,24128,102208,126336,

%T 535168,661504,2802176,3463680,14672384,18136064,76825600,94961664,

%U 402264064,497225728,2106281984,2603507712

%N First row of spectral array W(sqrt(5)-1).

%H 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 Conjectures: a(n) = 6*a(n-2)-4*a(n-4). G.f.: -(x+1)*(4*x^2-4*x-1) / (4*x^4-6*x^2+1). - _Colin Barker_, Oct 23 2014

%o (PARI)

%o \\ The first row of the generalized Wythoff array W(h),

%o \\   where h is an irrational number between 1 and 2.

%o row1(h, m) = {

%o   my(

%o     a=vector(m, n, floor(n*h)),

%o     b=setminus(vector(m, n, n), a),

%o     w=[a[1]^2, b[a[1]]],

%o     j=3

%o   );

%o   while(1,

%o     if(j%2==1,

%o       if(w[j-1]<=#a, w=concat(w, a[w[j-1]]), return(w))

%o     ,

%o       if(w[j-2]<=#b, w=concat(w, b[w[j-2]]), return(w))

%o     );

%o     j++

%o   );

%o   w

%o }

%o row1(sqrt(5)-1, 100000) \\ _Colin Barker_, Oct 23 2014

%K nonn,more

%O 0,2

%A _Clark Kimberling_

%E a(14)-a(18) from _Colin Barker_, Oct 23 2014 and _Michel Marcus_, Oct 24 2014

%E a(19)-a(26) from _Sean A. Irvine_, May 14 2019