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%I #13 Jul 29 2023 02:59:15
%S 0,1,0,0,1,0,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0,0,1,0,0,
%T 1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0,1,0,1,0,0,0,1,0,0,1,0,0,1,
%U 0,1,0,0,0,1,0,0,1,0,0,0,1,0,1,0,0,0,1,0,0,1
%N Unique sequence with a(1)=0, a(2)=1, representing an array T(i,j) read by antidiagonals in which every row is this sequence itself.
%C All terms are either 0 or 1. 1's are always isolated (i.e., never adjacent). There are arbitrarily long runs of consecutive 0's (see A283325).
%H Ivan Neretin, <a href="/A283683/b283683.txt">Table of n, a(n) for n = 1..26796</a> (corrected by Ray Chandler, Jan 19 2019)
%H Clark Kimberling, <a href="http://faculty.evansville.edu/ck6/integer/fractals.html">Fractal sequences</a>
%H Clark Kimberling, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa73/aa7321.pdf">Numeration systems and fractal sequences</a>, Acta Arithmetica 73 (1995) 103-117.
%F a(n) = A020906(n) - 1. The positions of ones here (2, 5, 9, 11, 14, 17, ...) are given by A020907.- _Georg Fischer_, Jul 28 2023
%e The sequence begins: 0, 1, 0, 0, 1, 0, 0, 0, 1, 0...
%e It represents a rectangular array read by downward antidiagonals. Each row of the array is this sequence itself:
%e 0 1 0 0 1 0...
%e 0 1 0 0 1...
%e 0 1 0 0...
%e 0 1 0...
%e 0 1...
%e 0...
%e ...
%t Nest[Flatten@Table[#[[n - i]], {n, Length[#] + 1}, {i, n - 1}] &, {0, 1}, 4]
%Y Cf. A020906, A020907, A283681, A283682.
%K nonn,tabl,nice
%O 1
%A _Ivan Neretin_, Mar 14 2017
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