A360173 Irregular triangle (an infinite binary tree) read by rows. The tree has root node 0, in row n=0. Each node then has left child m - n if nonnegative and right child m + n. Where m is the value of the parent node and n is the row of the children.

0, 1, 3, 0, 6, 4, 2, 10, 9, 7, 5, 15, 3, 15, 1, 13, 11, 9, 21, 10, 8, 22, 8, 6, 20, 4, 18, 2, 16, 14, 28, 2, 18, 0, 16, 14, 30, 0, 16, 14, 12, 28, 12, 10, 26, 10, 8, 24, 6, 22, 20, 36, 11, 9, 27, 9, 7, 25, 5, 23, 21, 39, 9, 7, 25, 5, 23, 3, 21, 19, 37, 3, 21

Offset

0,3

Comments

A node will have a left child only if the value of that child is greater than or equal to 0. But, each node will have a right child, since adding n will always be greater than 0.

The n-th row will have A141002(n) nodes. The leftmost border is A008344 and the rightmost is A000217.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..9395 (rows for n = 0..17 flattened)

Example

The binary tree starts with root 0 in row n = 0. In row n = 3, the parent node m = 3 has the first left child since 3 - 3 >= 0.
The tree begins:
row
[n]
[0]           0
               \
[1]             1
                 \
[2]            ___3___
              /       \
             /         \
[3]         0         __6__
             \       /     \
[4]           4     2      10
               \     \    /  \
[5]             9     7  5    15

Maple

T:= proc(n) option remember; `if`(n=0, 0, map(x->
      [`if`(x<n, [][], x-n), x+n][], [T(n-1)])[])
    end:
seq(T(n), n=0..10);  # Alois P. Heinz, Jan 30 2023

Prog

(Python)
def A360173_rowlist(row_n):
    A = [[0]]
    for i in range(0, row_n):
        A.append([])
        for j in range(0, len(A[i])):
            x = A[i][j]
            if x - i -1 >= 0:
                A[i+1].append(x-i-1)
            if x + i + 1 >= 0:
                A[i+1].append(x+i+1)
    return(A)
(PARI) row(n) = { my (r=[0]); for (h=1, n, r=concat(apply(v->if (v-h>=0, [v-h, v+h], [v+h]), r))); return (r) } \\ Rémy Sigrist, Jan 31 2023

Crossrefs

Cf. A000217, A008344, A141001, A141002.

Row sums give A360229.

Sequence in context: A088162 A133170 A062542 * A109693 A188858 A199610

Adjacent sequences: A360170 A360171 A360172 * A360174 A360175 A360176

Keyword

nonn,look,tabf,easy

Author

John Tyler Rascoe, Jan 28 2023

Status

approved