A308178 -id:A308178 - cp's OEIS frontend

A308179 The triangle defined in A308178, but read across rows.

0, 1, 3, 2, 0, 5, 3, 1, 4, 2, 4, 2, 0, 3, 1, 5, 7, 1, 4, 2, 6, 6, 4, 2, 0, 3, 5, 7, 7, 5, 3, 1, 4, 10, 8, 11, 8, 6, 7, 9, 0, 11, 5, 10, 4, 9, 11, 10, 8, 6, 3, 13, 7, 15, 12, 10, 8, 6, 5, 9, 0, 14, 12, 11, 7, 18, 11, 9, 12, 7, 8, 1, 10, 5, 6, 15, 13, 14, 12, 10, 8, 6, 5, 2, 0, 14, 9, 16, 17, 11, 13

Offset: 0

N. J. A. Sloane, May 28 2019

Column y=1 is A263313; the main diagonal is A308180.

After 13 steps, the y=2 column appears to become quasi-periodic with a saltus of 4. That is, the first differences appear to become periodic with period (-1, -2, 1, 6).

			Start of chessboard showing antidiagonals 0 through 12:
y =  0, 1, 2, 3, 4, 5, 6, 7, ...
--------------------------------
x=0  0,
x=1  1, 3,
x=2  2, 0, 5,
x=3  3, 1, 4, 2,
x=4  4, 2, 0, 3, 1,
x=5  5, 7, 1, 4, 2, 6,
x=6  6, 4, 2, 0, 3, 5, 7,
x=7  7, 5, 3, 1, 4, 10, ...,
x=8  8, 6, 7, 9, 0, ...,
x=9  9, 11, 10, 8, ...,
x=10 10, 8, 6, ...,
x=11 11, 9, ...,
x=12 12, ...,
x=13 ...,

Rémy Sigrist, Table of n, a(n) for n = 0..11475 (rows for x = 0..150)

Cf. A308178, A263313, A308180.

More terms from Rémy Sigrist, May 29 2019

A308180 Main diagonal of triangle defined in A308178.

Original entry on oeis.org

0, 3, 5, 2, 1, 6, 7, 11, 4, 12, 18, 14, 13, 8, 17, 9, 22, 23, 25, 29, 10, 28, 19, 30, 38, 31, 39, 15, 47, 24, 16, 40, 34, 42, 50, 51, 41, 44, 46, 49, 58, 55, 45, 21, 66, 69, 20, 56, 65, 60, 73, 67, 77, 57, 78, 63, 79, 70, 26, 27, 85, 87, 93, 76, 82, 89, 71

Offset: 0

N. J. A. Sloane, May 28 2019

nonn

Theorem: This is a permutation of the nonnegative integers. [The proof is analogous to that for A286295.]

Conjecture: There is a unique fixed point at n=0, and the positive integers form one "cycle", namely (... 59 27 15 9 12 13 8 4 1 3 2 5 6 7 11 14 17 23 30 16 22 19 29 24 38 ...).

Rémy Sigrist, Table of n, a(n) for n = 0..5000

Cf. A308178, A308179, A286295.

More terms from Rémy Sigrist, May 29 2019

cp's OEIS Frontend

A308179 The triangle defined in A308178, but read across rows.

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