A240813 - OEIS

%I #19 Oct 25 2014 01:28:40

%S 6,0,14,164,54,13,0,0,10,11,60,37,11,12,13,2354,30,13,13,14,15,282,63,

%T 44,14,15,17,18,1336,368,31,15,17,18,19,20,100,47,49,17,18,19,20,21,

%U 22,1254,46,38,18,19,20,21,22,23,24,366,108,80,19,20,21,22,23

%N 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.

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

%D 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.

%H Lars Blomberg, <a href="/A240813/b240813.txt">Table of n, a(n) for n = 1..10000</a>, "infinity" = 10^8.

%H B. Balamohan, A. Kuznetsov and S. Tanny, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL10/Tanny/tanny3.html">On the behavior of a variant of Hofstadter's Q-sequence</a>, J. Integer Sequences, Vol. 10 (2007), #07.7.1.

%H 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; <a href="https://vimeo.com/91708646">Part 1</a>, <a href="https://vimeo.com/91710600">Part 2</a>.

%H <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>

%e Triangle begins:

%e 6,

%e 0, 14,

%e 164, 54, 13,

%e 0, 0, 10, 11,

%e 60, 37, 11, 12, 13,

%e 2354, 30, 13, 13, 14, 15,

%e 282, 63, 44, 14, 15, 17, 18,

%e 1336, 368, 31, 15, 17, 18, 19

%e ...

%Y Diagonals give A134680, A240811, A240812.

%Y See A240816 for another version.

%K nonn,tabl

%O 1,1

%A _N. J. A. Sloane_, Apr 15 2014

%E More terms from _Lars Blomberg_, Oct 24 2014