A329934 a(1)=1, a(2)=1, a(n) = (number of times a(n-1) has appeared before) + (number of times a(n-2) has appeared before).

1, 1, 4, 3, 2, 2, 4, 4, 6, 4, 5, 5, 4, 7, 6, 3, 4, 8, 7, 3, 5, 6, 6, 8, 6, 7, 8, 6, 9, 7, 5, 8, 8, 10, 6, 8, 13, 7, 6, 13, 10, 4, 9, 9, 6, 12, 10, 4, 11, 9, 5, 9, 10, 9, 10, 11, 7, 8, 13, 10, 9, 13, 11, 7, 10, 14, 8, 9, 16, 9, 10, 17, 9, 11, 14, 6, 12, 12, 6, 14, 14

Offset

1,3

Comments

Conjecture: This sequence grows logarithmically.

Links

Joshua Oliver, Table of n, a(n) for n = 1..4000

Rémy Sigrist, Density plot of the first 10000000 terms

Example

a(n)=4 where n=3 because 1 (a(n-1)) has appeared twice before, and 1 (a(n-2)) has appeared twice before as well. 2+2 = 4.

Maple

b:= proc(n) option remember; `if`(n=0, 0, b(n-1)+x^a(n)) end:
a:= proc(n) option remember; `if`(n<3, 1, (p->
      coeff(p, x, a(n-1))+coeff(p, x, a(n-2)))(b(n-1)))
    end:
seq(a(n), n=1..120);  # Alois P. Heinz, Nov 24 2019

Mathematica

A={1, 1}; For[n=3, n<=81, n++, A=Append[A, Sum[Count[Table[Part[A, i], {i, 1, n-1}], Part[A, n-k]], {k, 2}]]]; A

Prog

(PARI) o=vector(17); for (n=1, 81, print1 (v=if (n<3, 1, o[pp]+o[p]) ", "); o[v]++; [pp, p]=[p, v]) \\ Rémy Sigrist, Nov 27 2019

Crossrefs

Cf. A158416, A306246, A316774.

Sequence in context: A109496 A138851 A181061 * A269611 A090342 A010307

Adjacent sequences: A329931 A329932 A329933 * A329935 A329936 A329937

Keyword

nonn

Author

Joshua Oliver, Nov 24 2019

Status

approved