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A360255
Irregular triangle (an infinite binary tree) read by rows: see Comments section for definition.
1
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
KEYWORD
nonn,tabf
AUTHOR
John Tyler Rascoe, Jan 30 2023
STATUS
approved