A240813 Triangle read by rows: T(n,k) (n >= 1, 1 <= k <= n) = length (or lifetime) of the meta-Fibonacci sequence f(1) = ... = f(n) = 1; f(i)=f(i-f(i-k))+f(i-f(i-n)) if that sequence is only defined for finitely many terms, or 0 if that sequence is infinite.

6, 0, 14, 164, 54, 13, 0, 0, 10, 11, 60, 37, 11, 12, 13, 2354, 30, 13, 13, 14, 15, 282, 63, 44, 14, 15, 17, 18, 1336, 368, 31, 15, 17, 18, 19, 20, 100, 47, 49, 17, 18, 19, 20, 21, 22, 1254, 46, 38, 18, 19, 20, 21, 22, 23, 24, 366, 108, 80, 19, 20, 21, 22, 23

Offset

1,1

Comments

The zero entries (except T(4,1)) are only conjectural.

References

D. R. Hofstadter, Curious patterns and non-patterns in a family of meta-Fibonacci recursions, Lecture in Doron Zeilberger's Experimental Mathematics Seminar, Rutgers University, April 10 2014.

Links

Lars Blomberg, Table of n, a(n) for n = 1..10000, "infinity" = 10^8.

B. Balamohan, A. Kuznetsov and S. Tanny, On the behavior of a variant of Hofstadter's Q-sequence, J. Integer Sequences, Vol. 10 (2007), #07.7.1.

D. R. Hofstadter, Curious patterns and non-patterns in a family of meta-Fibonacci recursions, Lecture in Doron Zeilberger's Experimental Mathematics Seminar, Rutgers University, April 10 2014; Part 1, Part 2.

Index entries for Hofstadter-type sequences

Example

Triangle begins:
6,
0, 14,
164, 54, 13,
0, 0, 10, 11,
60, 37, 11, 12, 13,
2354, 30, 13, 13, 14, 15,
282, 63, 44, 14, 15, 17, 18,
1336, 368, 31, 15, 17, 18, 19
...

Crossrefs

Diagonals give A134680, A240811, A240812.

See A240816 for another version.

Sequence in context: A240821 A320146 A283999 * A175567 A069828 A340951

Adjacent sequences: A240810 A240811 A240812 * A240814 A240815 A240816

Keyword

nonn,tabl

Author

N. J. A. Sloane, Apr 15 2014

Extensions

More terms from Lars Blomberg, Oct 24 2014

Status

approved