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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, 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
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
KEYWORD
nonn
AUTHOR
Nathan Fox and Altug Alkan, Jul 08 2018
STATUS
approved