A279406 Irregular triangle read by rows: T(n,k) (n>=1, 0 <= k <= n^2) = minimal number of squares attacked by k queens on an n X n toroidal board.

0, 1, 0, 4, 4, 4, 4, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 12, 14, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 0, 17, 22, 23, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 0, 20, 26, 30, 30, 32, 32, 34, 34, 34

Offset: 1

Author

Andrey Zabolotskiy, Dec 11 2016

Keywords

• nonn
• tabf

Comments

A279405(n) is maximal m such that T(n,m) >= m.

Generally, T(n,k') <= n^2-k if and only if T(n,k) <= n^2-k'.

Examples

			The triangle begins:
0 1
0 4 4 4 4
0 9 9 9 9 9 9 9 9 9
0 12 14 15 15 16 16 16 16 16 16 16 16 16 16 16 16
		

Links

• Andrey Zabolotskiy, First 9 rows of the triangle and a part of row 10

Crossrefs

Cf. A000290, A250000, A274947, A274948, A279405, A279403.

Formula

T(n,0) = 0.

T(n,k) = A000290(n) for k > A000290(n) - T(n,1).

T(n,1) = A047461(n) = A000290(n) - A279403(n,1).