A308881 Irregular array read by rows: row k (k>=1) contains k^2 numbers, formed by filling in a k X k square by upwards antidiagonals so entries in all rows, columns, diagonals, antidiagonals are distinct, and then reading that square across rows.

0, 0, 2, 1, 3, 0, 2, 1, 1, 3, 4, 2, 0, 5, 0, 2, 1, 5, 1, 3, 4, 0, 2, 0, 5, 1, 3, 1, 2, 4, 0, 2, 1, 5, 3, 1, 3, 4, 0, 6, 2, 0, 5, 1, 7, 3, 1, 2, 4, 0, 4, 5, 0, 3, 1, 0, 2, 1, 5, 3, 4, 1, 3, 4, 0, 7, 2, 2, 0, 5, 1, 6, 9, 3, 1, 2, 4, 0, 5, 4, 6, 0, 3, 1, 7, 5, 7, 8, 6, 4, 10

Offset

1,3

Comments

The first row of the k X k square converges to A295563 as k increases.

When filling in the k X k square, always choose the smallest possible number. Each k X k square is uniquely determined.

Links

I. V. Serov, Rows of first 32 squares, flattened (There are 1^2+2^2+...+32^2 = 11440 entries.)

F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, Queens in exile: non-attacking queens on infinite chess boards, Electronic J. Combin., 27:1 (2020), #P1.52.

Example

The first eight squares are (here A=10, B=11, C=12):
0
--------
02
13
--------
021
134
205
--------
0215
1340
2051
3124
--------
02153
13406
20517
31240
45031
--------
021534
134072
205169
312405
460317
57864A
--------
0215349
1340725
2051864
3124058
4603172
5786493
6432587
--------
0215349A
13407258
20518643
31240786
4603152B
5786493C
64325879
756893A2
--------

Crossrefs

Cf. A295563, A308880.

Sequence in context: A125073 A350387 A325310 * A281488 A071461 A091829

Adjacent sequences: A308878 A308879 A308880 * A308882 A308883 A308884

Keyword

nonn,tabf

Author

N. J. A. Sloane, Jun 29 2019

Status

approved