

A316628


a(1)=1, a(2)=2, a(3)=2, a(4)=3; a(n) = a(na(n1))+a(n1a(n2)a(n2a(n2))) for n > 4.


4



1, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 6, 7, 7, 8, 8, 8, 8, 8, 9, 10, 10, 11, 11, 11, 12, 13, 13, 13, 13, 13, 13, 14, 15, 15, 16, 16, 16, 17, 18, 18, 18, 18, 19, 20, 20, 21, 21, 21, 21, 21, 21, 21, 22, 23, 23, 24, 24, 24, 25, 26, 26, 26, 26, 27, 28, 28, 29, 29, 29, 29, 29, 30, 31, 31
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OFFSET

1,2


COMMENTS

This sequence increases slowly.
k occurs A035612(k) times.
Each Fibonacci number occurs more times than any number before it.


LINKS

Nathan Fox, Table of n, a(n) for n = 1..10000
Nathan Fox, Trees, Fibonacci Numbers, and Nested Recurrences, Rutgers University Experimental Math Seminar, Mar 07, 2019


FORMULA

a(n+1)a(n)=1 or 0.
a(n)/n > C=(sqrt(5)1)/(sqrt(5)+1).


MAPLE

A316628:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 1: elif n = 2 then 2: elif n = 3 then 2: elif n = 4 then 3: else A316628(nA316628(n1)) + A316628(n1A316628(n2)A316628(n2A316628(n2))): fi: end:


PROG

(MAGMA) I:=[1, 2, 2, 3]; [n le 4 select I[n] else Self(nSelf(n1))+Self(n1Self(n2)Self(n2Self(n2))): n in [1..100]]; // Vincenzo Librandi, Jul 09 2018
(GAP) a:=[1, 2, 2, 3];; for n in [5..80] do a[n]:=a[na[n1]]+a[n1a[n2]a[n2a[n2]]]; od; a; # Muniru A Asiru, Jul 09 2018


CROSSREFS

Cf. A000045, A005185, A035612, A046699.
Sequence in context: A166079 A269381 A080677 * A153112 A005350 A055037
Adjacent sequences: A316625 A316626 A316627 * A316629 A316630 A316631


KEYWORD

nonn


AUTHOR

Nathan Fox, Jul 08 2018


STATUS

approved



