A330332 a(n) = (number of times a(n-1) has already appeared) + (number of times a(n-2) has already appeared) + (number of times a(n-3) has already appeared), starting with a(n) = n for n<3.

0, 1, 2, 3, 3, 5, 5, 6, 5, 7, 5, 9, 6, 7, 5, 9, 9, 11, 7, 7, 9, 12, 9, 11, 8, 8, 6, 7, 10, 9, 12, 9, 16, 10, 10, 7, 12, 12, 14, 9, 13, 10, 13, 8, 9, 14, 14, 15, 7, 11, 11, 15, 10, 11, 12, 15, 13, 11, 12, 15, 16, 12, 13, 13, 17, 11, 13, 14, 17, 12, 14, 15, 18, 11, 14, 15, 20, 13, 14, 15, 21, 15

Offset: 0

Author

N. J. A. Sloane, Dec 14 2019

Keywords

• nonn
• look

Comments

Generalizes A316774, which looks at the frequencies of the two previous terms. Here we look at three previous terms.

If we look at just one previous term, we get 0, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, ..., which is A133622 prefixed by 0, 1, or A152271 with its initial 1 changed to 0.

Links

• N. J. A. Sloane, Table of n, a(n) for n = 0..10000
• Rémy Sigrist, Density plot of the first 2^22 terms

Crossrefs

Cf. A316774, A133622, A152271.

Programs

Maple

b:= proc() 0 end:
a:= proc(n) option remember; local t;
      t:= `if`(n<3, n, b(a(n-1))+b(a(n-2))+b(a(n-3)));
      b(t):= b(t)+1; t
    end:
[seq(a(n), n=0..200)]; # Following Alois P. Heinz's program for A316774

Mathematica

b[_] = 0;
a[n_] := a[n] = Module[{t}, t = If[n<3, n, b[a[n-1]] + b[a[n-2]] + b[a[n-3]]]; b[t]++; t];
a /@ Range[0, 200] (* Jean-François Alcover, Nov 09 2020, after Maple *)