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A363930 Irregular table T(n, k), n >= 0, k = 1..A363710(n), read by rows; the n-th row lists the nonnegative numbers m <= n such that A003188(m) AND A003188(n-m) = 0 (where AND denotes the bitwise AND operator).

%I A363930 #9 Jun 30 2023 01:01:40
%S A363930 0,0,1,0,2,0,3,0,1,3,4,0,1,4,5,0,6,0,7,0,1,7,8,0,1,2,3,6,7,8,9,0,2,3,
%T A363930 7,8,10,0,3,8,11,0,1,3,9,11,12,0,1,12,13,0,14,0,15,0,1,15,16,0,1,2,3,
%U A363930 14,15,16,17,0,2,3,4,6,12,14,15,16,18,0,3,4,7,12,15,16,19
%N A363930 Irregular table T(n, k), n >= 0, k = 1..A363710(n), read by rows; the n-th row lists the nonnegative numbers m <= n such that A003188(m) AND A003188(n-m) = 0 (where AND denotes the bitwise AND operator).
%C A363930 This sequence is related to the T-square fractal (see A363710).
%H A363930 Rémy Sigrist, <a href="/A363930/b363930.txt">Table of n, a(n) for n = 0..13126</a> (rows for n = 0..2^9 flattened)
%H A363930 Wikipedia, <a href="https://en.wikipedia.org/wiki/T-square_(fractal)">T-square (fractal)</a>
%F A363930 T(n, 1) = 0.
%F A363930 T(n, A363710(n)) = n.
%F A363930 T(n, k) + T(n, A363710(n)+1-k) = n.
%e A363930 Table T(n, k) begins:
%e A363930   n   n-th row
%e A363930   --  ----------------------
%e A363930    0  0
%e A363930    1  0, 1
%e A363930    2  0, 2
%e A363930    3  0, 3
%e A363930    4  0, 1, 3, 4
%e A363930    5  0, 1, 4, 5
%e A363930    6  0, 6
%e A363930    7  0, 7
%e A363930    8  0, 1, 7, 8
%e A363930    9  0, 1, 2, 3, 6, 7, 8, 9
%e A363930   10  0, 2, 3, 7, 8, 10
%e A363930   11  0, 3, 8, 11
%e A363930   12  0, 1, 3, 9, 11, 12
%e A363930   13  0, 1, 12, 13
%e A363930   14  0, 14
%e A363930   15  0, 15
%e A363930   16  0, 1, 15, 16
%o A363930 (PARI) row(n) = { select (m -> bitand(bitxor(m, m\2), bitxor(n-m, (n-m)\2))==0, [0..n]) }
%Y A363930 See A295989, A353174 and A362327 for similar sequences.
%Y A363930 Cf. A003188, A363710.
%K A363930 nonn,base,tabf
%O A363930 0,5
%A A363930 _Rémy Sigrist_, Jun 28 2023