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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.

%I A240821 #21 Oct 25 2014 01:28:20
%S A240821 6,0,13,162,29,20,0,0,71,27,56,29,34,35,28,2349,24,0,28,54,41,276,50,
%T A240821 46,44,34,55,40,1300,0,34,0,37,68,89,44,84,332,36,60,56,43,80,93,54,
%U A240821 1245,56,39,44,0,48,48,71,87,57,356,848,90,46,74,68,51,55,227
%N 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.
%C A240821 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.
%D A240821 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 A240821 Lars Blomberg, <a href="/A240821/b240821.txt">Table of n, a(n) for n = 1..10000</a>, "infinity" = 10^8.
%H A240821 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 A240821 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 A240821 <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>
%e A240821 Triangle begins:
%e A240821 6,
%e A240821 0, 13,
%e A240821 162, 29, 20,
%e A240821 0, 0, 71, 27,
%e A240821 56, 29, 34, 35, 28,
%e A240821 2349, 24, 0, 28, 54, 41,
%e A240821 276, 50, 46, 44, 34, 55, 40,
%e A240821 1300, 0, 34, 0, 37, 68, 89, ...
%e A240821 ...
%Y A240821 Diagonals give A240818, A240819, A240820.
%Y A240821 See A240825 for another version.
%K A240821 nonn,tabl
%O A240821 1,1
%A A240821 _N. J. A. Sloane_, Apr 15 2014
%E A240821 More terms from _Lars Blomberg_, Oct 24 2014