A283683 - OEIS

%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