

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.


2



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
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OFFSET

1,4


COMMENTS

A279405(n) is maximal m such that T(n,m) >= m.
Generally, T(n,k') <= n^2k if and only if T(n,k) <= n^2k'.


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



