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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). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 9 05:12 EDT 2020. Contains 336319 sequences. (Running on oeis4.)