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.

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

Author

N. J. A. Sloane, Jul 02 2014

Keywords

• nonn

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.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Index entries for Hofstadter-type sequences

Crossrefs

A006949, A240807, A240808 use the same recurrence.

See also A244479 (a(n)/2).

Programs

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

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 *)