A240829 a(1)=-1, a(2)=0, a(3)=1; thereafter a(n) = Sum(a(n-i-s-a(n-i-1)),i=0..k-1) where s=0, k=3.

-1, 0, 1, 3, 2, 4, 4, 7, 4, 7, 7, 9, 8, 9, 11, 10, 10, 13, 15, 13, 13, 13, 18, 15, 18, 18, 18, 18, 18, 23, 23, 20, 19, 23, 28, 27, 23, 25, 27, 28, 25, 26, 28, 30, 31, 32, 33, 33, 32, 34, 33, 38, 36, 39, 34, 36, 36, 39, 39, 39, 39, 44, 46, 46, 43, 46, 46, 44, 44, 49, 49, 49, 46, 51, 48, 51, 51, 54, 54, 54, 54, 54

Offset: 1

Author

N. J. A. Sloane, Apr 16 2014

Keywords

• sign
• hear

References

• Callaghan, Joseph, John J. Chew III, and Stephen M. Tanny. "On the behavior of a family of meta-Fibonacci sequences." SIAM Journal on Discrete Mathematics 18.4 (2005): 794-824. See Fig. 1.7.

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..20000
• Index entries for Hofstadter-type sequences

Crossrefs

Same recurrence as A240828, A120503 and A046702.

Programs

Maple

#T_s,k(n) from Callaghan et al. Eq. (1.6).
s:=0; k:=3;
a:=proc(n) option remember; global s,k;
if n <= 3 then n-2
else
    add(a(n-i-s-a(n-i-1)),i=0..k-1);
fi; end;
t1:=[seq(a(n),n=1..100)];