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A244478
a(0)=2, a(1)=0, a(2)=2; thereafter a(n) = a(n-1-a(n-1))+a(n-2-a(n-2)) unless a(n-1) <= n-1 or a(n-2) <= n-2 in which case the sequence terminates.
3
2, 0, 2, 2, 2, 2, 4, 4, 4, 4, 4, 6, 6, 6, 8, 8, 8, 8, 8, 8, 10, 10, 10, 12, 12, 12, 12, 14, 14, 14, 16, 16, 16, 16, 16, 16, 16, 18, 18, 18, 20, 20, 20, 20, 22, 22, 22, 24, 24, 24, 24, 24, 26, 26, 26, 28, 28, 28, 28, 30, 30, 30, 32, 32, 32, 32, 32, 32, 32, 32, 34, 34, 34, 36, 36, 36, 36, 38, 38, 38
OFFSET
0,1
REFERENCES
Higham, J.; Tanny, S. More well-behaved meta-Fibonacci sequences. Proceedings of the Twenty-fourth Southeastern International Conference on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1993). Congr. Numer. 98(1993), 3-17. See Prop. 2.1.
MAPLE
f := proc(n) option remember;
if n=0 then 2
elif n=1 then 0
elif n=2 then 2
else
f(n-1-f(n-1))+f(n-2-f(n-2));
fi;
end proc;
[seq(f(n), n=0..2000)];
MATHEMATICA
f[n_] := f[n] = Switch[n, 0, 2, 1, 0, 2, 2, _,
f[n-1-f[n-1]]+f[n-2-f[n-2]]];
Table[f[n], {n, 0, 100}] (* Jean-François Alcover, Oct 02 2024 *)
PROG
(Haskell)
a244478 n = a244478_list !! n
a244478_list = 2 : 0 : 2 : zipWith (+) xs (tail xs)
where xs = map a244478 $ zipWith (-) [1..] $ tail a244478_list
-- Reinhard Zumkeller, Jul 05 2014
CROSSREFS
A006949, A240807, A240808 use the same recurrence.
See also A244479 (a(n)/2).
Sequence in context: A161872 A278248 A036461 * A261153 A374078 A199123
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 02 2014
STATUS
approved