A240821 Triangle read by rows: T(n,k) (n >= 1, 1 <= k <= n) = length (or lifetime) of the meta-Fibonacci sequence {f(i) = i for i <= n; 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, 13, 162, 29, 20, 0, 0, 71, 27, 56, 29, 34, 35, 28, 2349, 24, 0, 28, 54, 41, 276, 50, 46, 44, 34, 55, 40, 1300, 0, 34, 0, 37, 68, 89, 44, 84, 332, 36, 60, 56, 43, 80, 93, 54, 1245, 56, 39, 44, 0, 48, 48, 71, 87, 57, 356, 848, 90, 46, 74, 68, 51, 55, 227

Offset: 1

Author

N. J. A. Sloane, Apr 15 2014

Keywords

• nonn
• tabl

Comments

The zero entries are only conjectural. More precisely, Hofstadter conjectures that T(n,k) = 0 (i.e. the sequence is immortal) iff n = 2k or n = 4k.

Examples

			Triangle begins:
6,
0, 13,
162, 29, 20,
0, 0, 71, 27,
56, 29, 34, 35, 28,
2349, 24, 0, 28, 54, 41,
276, 50, 46, 44, 34, 55, 40,
1300, 0, 34, 0, 37, 68, 89, ...
...
		

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

Crossrefs

Diagonals give A240818, A240819, A240820.

See A240825 for another version.

Extensions

More terms from Lars Blomberg, Oct 24 2014