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

0,3

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

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 *)

Crossrefs

Cf. A316774, A133622, A152271.

Sequence in context: A262319 A262488 A278530 * A023816 A353714 A159237

Adjacent sequences: A330329 A330330 A330331 * A330333 A330334 A330335

Keyword

nonn,look

Author

N. J. A. Sloane, Dec 14 2019

Status

approved