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

1,1

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.

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, 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, ...
...

Crossrefs

Diagonals give A240818, A240819, A240820.

See A240825 for another version.

Sequence in context: A028603 A205966 A183772 * A320146 A283999 A240813

Adjacent sequences: A240818 A240819 A240820 * A240822 A240823 A240824

Keyword

nonn,tabl

Author

N. J. A. Sloane, Apr 15 2014

Extensions

More terms from Lars Blomberg, Oct 24 2014

Status

approved