A317389 a(0) = 0, a(1) = a(2) = 1; for n >= 3, a(n) = freq(a(g(n)),n)*freq(a(n-g(n)),n) where g = A000195 and freq(i, j) is the number of times i appears in the terms a(0) .. a(j-1).

0, 1, 1, 4, 2, 2, 4, 4, 6, 6, 4, 4, 10, 10, 4, 4, 14, 14, 4, 4, 18, 81, 81, 9, 18, 18, 9, 27, 27, 18, 18, 18, 54, 54, 54, 27, 27, 27, 45, 45, 45, 27, 27, 27, 72, 72, 72, 27, 27, 27, 99, 99, 99, 27, 27, 6, 6, 26, 26, 8, 8, 4, 4, 4, 4, 26, 26, 26, 26, 12, 12, 12, 12, 8, 8, 8, 8, 12, 12, 12, 12, 16, 16, 16, 16, 8, 8, 8, 8, 20, 20, 20

Offset: 0

Author

Altug Alkan, Jul 27 2018

Keywords

• nonn
• look

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..65536

Crossrefs

Cf. A317359.

Programs

Maple

b:= proc() 0 end:
a:= proc(n) option remember; local t;
      t:= `if`(n<3, n*(3-n)/2, b(a(ilog(n)))*b(a(n-ilog(n))));
      b(t):= b(t)+1; t
    end:
seq(a(n), n=0..200);  # Alois P. Heinz, Jul 27 2018

Mathematica

b[_] = 0;
a[n_] := a[n] = Module[{t}, t = If[n<3, n(3-n)/2, b[a[Floor@Log[n]]] b[a[n - Floor@Log[n]]]]; b[t] = b[t]+1; t];
a /@ Range[0, 200] (* Jean-François Alcover, Nov 27 2020, after Alois P. Heinz *)