A022165 First row of spectral array W(sqrt(5)-1).

1, 5, 6, 26, 32, 136, 168, 712, 880, 3728, 4608, 19520, 24128, 102208, 126336, 535168, 661504, 2802176, 3463680, 14672384, 18136064, 76825600, 94961664, 402264064, 497225728, 2106281984, 2603507712

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• more

Links

• A. Fraenkel and C. Kimberling, Generalized Wythoff arrays, shuffles and interspersions, Discrete Mathematics 126 (1994) 137-149.

Programs

PARI

\\ The first row of the generalized Wythoff array W(h),
\\   where h is an irrational number between 1 and 2.
row1(h, m) = {
  my(
    a=vector(m, n, floor(n*h)),
    b=setminus(vector(m, n, n), a),
    w=[a[1]^2, b[a[1]]],
    j=3
  );
  while(1,
    if(j%2==1,
      if(w[j-1]<=#a, w=concat(w, a[w[j-1]]), return(w))
    ,
      if(w[j-2]<=#b, w=concat(w, b[w[j-2]]), return(w))
    );
    j++
  );
  w
}
row1(sqrt(5)-1, 100000) \\ Colin Barker, Oct 23 2014

Formula

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

Extensions

a(14)-a(18) from Colin Barker, Oct 23 2014 and Michel Marcus, Oct 24 2014

a(19)-a(26) from Sean A. Irvine, May 14 2019