A308178 Scan an infinite 45-degree triangular chessboard (cells (x,y) with 0 <= y <= x) by upwards antidiagonals, filling in each cell with the smallest nonnegative number already placed that cannot be seen by a chess queen at (x,y); sequence gives numbers along the successive antidiagonals.

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

Offset: 0

Author

N. J. A. Sloane, May 28 2019

Keywords

• nonn
• tabf

Comments

The 0's occur in positions (x,y) = (2k,k), k >= 0.

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).

There is a very similar triangle in A274650.

Examples

			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 ...,
The first few antidiagonals are:
0,
1,
2, 3,
3, 0,
4, 1, 5,
5, 2, 4,
6, 7, 0, 2,
7, 4, 1, 3,
8, 5, 2, 4, 1,
9, 6, 3, 0, 2,
...
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10200 (antidiagonals for x+y = 0..200)
• Rémy Sigrist, Colored representation of the first 1000 antidiagonals (black pixels correspond to zeros)
• Rémy Sigrist, PARI program for A308178

Crossrefs

Reading the triangle across rows gives A308179.

Cf. A263313, A274650, A308180

Programs

PARI

See Links section.

Extensions

More terms from Rémy Sigrist, May 29 2019