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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 (list; graph; refs; listen; history; text; internal format)
 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(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 Cf. A000045, A005185, A035612, A046699. Sequence in context: A269381 A080677 A344497 * A153112 A005350 A055037 Adjacent sequences:  A316625 A316626 A316627 * A316629 A316630 A316631 KEYWORD nonn AUTHOR Nathan Fox, Jul 08 2018 STATUS approved

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Last modified October 2 18:53 EDT 2022. Contains 357228 sequences. (Running on oeis4.)