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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.

%I A240813 #19 Oct 25 2014 01:28:40
%S A240813 6,0,14,164,54,13,0,0,10,11,60,37,11,12,13,2354,30,13,13,14,15,282,63,
%T A240813 44,14,15,17,18,1336,368,31,15,17,18,19,20,100,47,49,17,18,19,20,21,
%U A240813 22,1254,46,38,18,19,20,21,22,23,24,366,108,80,19,20,21,22,23
%N 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.
%C A240813 The zero entries (except T(4,1)) are only conjectural.
%D A240813 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 A240813 Lars Blomberg, <a href="/A240813/b240813.txt">Table of n, a(n) for n = 1..10000</a>, "infinity" = 10^8.
%H A240813 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 A240813 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 A240813 <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>
%e A240813 Triangle begins:
%e A240813 6,
%e A240813 0, 14,
%e A240813 164, 54, 13,
%e A240813 0, 0, 10, 11,
%e A240813 60, 37, 11, 12, 13,
%e A240813 2354, 30, 13, 13, 14, 15,
%e A240813 282, 63, 44, 14, 15, 17, 18,
%e A240813 1336, 368, 31, 15, 17, 18, 19
%e A240813 ...
%Y A240813 Diagonals give A134680, A240811, A240812.
%Y A240813 See A240816 for another version.
%K A240813 nonn,tabl
%O A240813 1,1
%A A240813 _N. J. A. Sloane_, Apr 15 2014
%E A240813 More terms from _Lars Blomberg_, Oct 24 2014