A240807 a(0)=a(1)=-1, 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.

-1, -1, 2, 1, 1, 3, 3, 3, 2, 4, 6, 4, 4, 5, 4, 8, 9, 6, 7, 8, 8, 8, 9, 10, 10, 9, 13, 14, 10, 12, 13, 12, 14, 15, 14, 15, 16, 16, 16, 17, 18, 18, 19, 20, 20, 20, 19, 23, 24, 20, 22, 22, 22, 25, 23, 22, 27, 27, 25, 28, 27, 27, 29, 29, 29, 29, 31, 31, 31, 32, 32, 32, 33, 34, 34, 35, 36, 36, 36, 37, 38, 38, 39, 40, 40, 40, 40, 39, 43, 44, 40, 42, 42, 42

Offset: 0

Author

N. J. A. Sloane, Apr 15 2014

Keywords

• sign

References

• Higham, Jeff and Tanny, Stephen, A tamely chaotic meta-Fibonacci sequence. Twenty-third Manitoba Conference on Numerical Mathematics and Computing (Winnipeg, MB, 1993). Congr. Numer. 99 (1994), 67-94.

Links

• N. J. A. Sloane, Table of n, a(n) for n = 0..20000
• Index entries for Hofstadter-type sequences

Crossrefs

A006949 and A240808 have the same recurrence but different initial conditions.

Programs

Haskell

a240807 n = a240807_list !! n
a240807_list = -1 : -1 : 2 : zipWith (+) xs (tail xs)
   where xs = map a240807 $ zipWith (-) [1..] $ tail a240807_list
-- Reinhard Zumkeller, Apr 17 2014

Maple

a:=proc(n) option remember;
if n = 0 then  -1
elif n = 1 then -1
elif n = 2 then 2
else
    if (a(n-1) <= n-1) and (a(n-2) <= n-2) then
    a(n-1-a(n-1))+a(n-2-a(n-2));
    else lprint("died with n =",n); return (-1);
    fi;
fi; end;
[seq(a(n),n=0..100)];

Mathematica

a[n_] := a[n] = Switch[n, 0, -1, 1, -1, 2, 2, _,
   If[a[n-1] <= n-1 && a[n-2] <= n-2,
   a[n-1-a[n-1]] + a[n-2-a[n-2]],
   Print["died with n =", n]; Return[-1]]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Oct 02 2024 *)