A360255 Irregular triangle (an infinite binary tree) read by rows: see Comments section for definition.

0, 1, 3, 6, 2, 10, 7, 5, 15, 13, 11, 9, 21, 20, 4, 18, 2, 16, 14, 28, 12, 28, 12, 26, 8, 24, 22, 20, 36, 21, 19, 37, 21, 17, 35, 17, 33, 13, 31, 11, 29, 27, 45, 11, 31, 9, 29, 27, 47, 31, 7, 27, 25, 45, 7, 27, 23, 43, 23, 41, 19, 39, 17, 37, 35, 55, 22, 42, 18

Offset

0,3

Comments

The binary tree has root node 0, in row n=0. The left child is m - n and the right child is m + n, where m is the parent node and n is the row of the child. A given node will only have a child if the child is nonnegative and the value of the child is not present in the path from the parent to the root, including the root value itself.

The n-th row will have A321535(n) nodes. The rightmost border is A000217.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..9517 (rows for n = 0..21 flattened)

Example

The binary tree starts with root 0 in row n = 0. In row n = 3, the parent node m = 3 does not have a left child since 3 - 3 = 0 is included in the path from the parent to the root {3,1,0}.
The tree begins:
row
[n]
[0]           0
               \
[1]             1
                 \
[2]               3
                   \
[3]               __6__
                 /     \
[4]             2      10
                 \    /  \
[5]               7  5    15

Prog

(MATLAB)
function a = A360255( max_row )
    p = 0; a = 0; pos = 1;
    for n = 1:max_row
        for k = pos:length(a)
            h =[]; o = p(k);
            while o > 0
                h = [h a(o)]; o = p(o);
            end
            if a(k)-n > 0
                if isempty(find(h == a(k)-n, 1))
                    p = [p k]; a = [a a(k)-n];
                end
            end
            if isempty(find(h == a(k)+n, 1))
                p = [p k]; a = [a a(k)+n];
            end
        end
        pos = k+1;
    end
end % Thomas Scheuerle, Jan 31 2023

Crossrefs

Cf. A000217, A141001, A141002, A321535, A360173.

Sequence in context: A309609 A266971 A257106 * A353989 A354087 A210187

Adjacent sequences: A360252 A360253 A360254 * A360256 A360257 A360258

Keyword

nonn,tabf

Author

John Tyler Rascoe, Jan 30 2023

Status

approved