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A316628
a(1)=1, a(2)=2, a(3)=2, a(4)=3; a(n) = a(n-a(n-1))+a(n-1-a(n-2)-a(n-2-a(n-2))) 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
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, 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(n-A316628(n-1)) + A316628(n-1-A316628(n-2)-A316628(n-2-A316628(n-2))): fi: end:
PROG
(Magma) I:=[1, 2, 2, 3]; [n le 4 select I[n] else Self(n-Self(n-1))+Self(n-1-Self(n-2)-Self(n-2-Self(n-2))): n in [1..100]]; // Vincenzo Librandi, Jul 09 2018
(GAP) a:=[1, 2, 2, 3];; for n in [5..80] do a[n]:=a[n-a[n-1]]+a[n-1-a[n-2]-a[n-2-a[n-2]]]; od; a; # Muniru A Asiru, Jul 09 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Nathan Fox, Jul 08 2018
STATUS
approved