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A240816 Triangle read by rows: T(n,k) (n >= 1, 1 <= k <= n) = index of first nonexisting term 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 A240816 #21 Jul 20 2021 03:11:43
%S A240816 7,0,15,165,55,14,0,0,11,12,61,38,12,13,14,2355,31,14,14,15,16,283,64,
%T A240816 45,15,16,18,19,1337,369,32,16,18,19,20
%N A240816 Triangle read by rows: T(n,k) (n >= 1, 1 <= k <= n) = index of first nonexisting term 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 A240816 The zero entries (except T(4,1)) are only conjectural.
%C A240816 Apart from the zero entries, equals A240813 + 1.
%H A240816 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 A240816 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 A240816 <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>
%e A240816 Triangle begins:
%e A240816      7;
%e A240816      0,  15;
%e A240816    165,  55, 14;
%e A240816      0,   0, 11, 12;
%e A240816     61,  38, 12, 13, 14;
%e A240816   2355,  31, 14, 14, 15, 16;
%e A240816    283,  64, 45, 15, 16, 18, 19;
%e A240816   1337, 369, 32, 16, 18, 19, 20, ?;
%e A240816   ...
%Y A240816 Diagonals give A240810, A240814, A240815.
%Y A240816 See A240813 for another version.
%K A240816 nonn,tabl,more
%O A240816 1,1
%A A240816 _N. J. A. Sloane_, Apr 15 2014