A316626 a(1)=a(2)=a(3)=1; a(n) = a(n-2*a(n-1))+a(n-1-2*a(n-2)) for n > 3.

1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20

Offset

1,4

Comments

This sequence increases slowly, and each term repeats at least three times.

If k is not a power of 2, then k appears in this sequence the same number of times as it appears in A081832. Otherwise, it appears exactly one additional time.

Links

Nathan Fox, Table of n, a(n) for n = 1..10000

A. Erickson, A. Isgur, B. W. Jackson, F. Ruskey and S. M. Tanny, Nested recurrence relations with Conolly-like solutions, See Conjecture 5.1.

Formula

a(n+1)-a(n)=1 or 0.

a(n)/n -> C=1/4.

Maple

A316626:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 1: elif n = 2 then 1: elif n = 3 then 1: else A316626(n-2*A316626(n-1)) + A316626(n-1-2*A316626(n-2)): fi: end:

Prog

(Magma) [n le 3 select 1  else Self(n-2*Self(n-1))+Self(n-1-2*Self(n-2)): n in [1..100]]; // Vincenzo Librandi, Jul 09 2018
(GAP) a:=[1, 1, 1];; for n in [4..80] do a[n]:=a[n-2*a[n-1]]+a[n-1-2*a[n-2]]; od; a; # Muniru A Asiru, Jul 09 2018

Crossrefs

Cf. A005185, A046699, A081832.

Sequence in context: A068063 A087181 A034973 * A269734 A066927 A060065

Adjacent sequences: A316623 A316624 A316625 * A316627 A316628 A316629

Keyword

nonn

Author

Nathan Fox and Altug Alkan, Jul 08 2018

Status

approved