

A240813


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


5



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
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OFFSET

1,1


COMMENTS

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


REFERENCES

D. R. Hofstadter, Curious patterns and nonpatterns in a family of metaFibonacci 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 Qsequence, J. Integer Sequences, Vol. 10 (2007), #07.7.1.
D. R. Hofstadter, Curious patterns and nonpatterns in a family of metaFibonacci recursions, Lecture in Doron Zeilberger's Experimental Mathematics Seminar, Rutgers University, April 10 2014; Part 1, Part 2.
Index entries for Hofstadtertype 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



