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

1,4

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'.

Links

Table of n, a(n) for n=1..70.

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

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).

Example

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

Crossrefs

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

Sequence in context: A268368 A274947 A331961 * A171408 A071907 A172369

Adjacent sequences: A279403 A279404 A279405 * A279407 A279408 A279409

Keyword

nonn,tabf

Author

Andrey Zabolotskiy, Dec 11 2016

Status

approved