A317191 Fill an n X n square array T(j,k), 1<=j<=n, 1=k<=n, by antidiagonals upwards in which each term is the least nonnegative integer satisfying the condition that no row, column, diagonal, or antidiagonal contains a repeated term; a(n) = T(n,n).

0, 3, 5, 4, 1, 10, 7, 2, 6, 8, 15, 12, 19, 17, 22, 23, 12, 26, 11, 31, 32, 12, 35, 10, 37, 42, 40, 45, 33, 49, 18, 17, 20, 53, 16, 51, 59, 18, 59, 60, 58, 64, 69, 69, 38, 29, 74, 26, 68, 78, 80, 36, 30, 33, 41, 39, 32, 33, 92, 41, 38, 89, 32, 35

Offset

1,2

Comments

This is the analog for an n X n board of the sequence A317190 (which is the main diagonal when we fill in the whole of the fourth quadrant in this way).

Links

Table of n, a(n) for n=1..64.

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

For n=3 the array T is
0 2 1
1 3 4
2 0 5
so a(3) = T(3,3) = 5.
For n=6 the array T is
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
so a(6) = T(6,6) = 10. This is the first time this sequence differs from A317190.

Crossrefs

Cf. A317190, A274318, A269529, A274528.

Sequence in context: A073006 A320029 A317190 * A165109 A349377 A349376

Adjacent sequences: A317188 A317189 A317190 * A317192 A317193 A317194

Keyword

nonn

Author

N. J. A. Sloane and Doron Zeilberger, Jul 30 2018

Status

approved