A279403 Irregular triangle read by rows: T(n,k) (n>=1, 0 <= k <= n^2) = minimal number of squares not attacked by k queens on an n X n toroidal board, with trailing zeros truncated.

1, 4, 9, 16, 4, 25, 8, 2, 36, 16, 4, 49, 24, 11, 4, 64, 36, 16, 6, 81, 48, 27, 12, 3, 100, 64, 36, 19, 4, 121, 80, 51, 29, 13, 144, 100, 64, 39, 16, 6, 169, 120, 83, 53, 29, 8, 2, 196, 144, 100, 67, 36, 18, 8, 225, 168, 223, 82, 41, 256, 196, 144, 103, 64, 40

Offset

1,2

Comments

Row lengths are A279402.

Links

Table of n, a(n) for n=1..65.

Formula

T(n,0) = A000290(n).

T(n,1) = A000290(n)-A047461(n) = A137932(n-1).

T(n,2) = A248825(n-4) for n >= 6.

Example

The triangle begins:
1 (0)
4 (0, 0, 0, 0)
9 (0, 0, ...)
16 4 (0, 0, ...)
25 8 2
36 16 4
49 24 11 4
64 36 16 6
81 48 27 12 3
100 64 36 19 4
121 80 51 29 13
144 100 64 39 16 6
169 120 83 53 29 8 2
196 144 100 67 36 18 8
225 168 123 82 41
256 196 144 103 64 40 ...

Crossrefs

Cf. A279402, A279406.

Sequence in context: A070444 A120866 A070443 * A330377 A070643 A070442

Adjacent sequences: A279400 A279401 A279402 * A279404 A279405 A279406

Keyword

nonn,tabf

Author

Andrey Zabolotskiy, Dec 11 2016

Status

approved