A278688 Triangle read by rows T(n, k) = number of non-equivalent ways to place k non-attacking ferses on an n X n board.

1, 1, 1, 1, 1, 1, 3, 6, 7, 6, 2, 1, 1, 3, 17, 45, 92, 99, 76, 27, 7, 1, 6, 43, 225, 832, 2102, 3773, 4860, 4643, 3356, 1868, 795, 248, 56, 8, 1, 1, 6, 84, 709, 4500, 19987, 66201, 164423, 314224, 465230, 540247, 492206, 352300, 195717, 83247, 26083, 5754, 780, 55

Offset: 1

Author

Heinrich Ludwig, Nov 27 2016

Keywords

• nonn
• tabf

Comments

The triangle T(n, k) is irregularly shaped: 0 <= k <= A093005(n), which means that A093005(n) is the maximal number of non-attacking ferses that can be placed on an n X n board. First row corresponds to n = 1. First column corresponds to k = 0.

Two placements that differ by rotation or reflection are counted only once.

A fers is a fairy chess piece attacking one step ne-nw-sw-se.

Examples

			Triangle begins:
1, 1;
1, 1,  1;
1, 3,  6,  7,  6,  2,  1;
1, 3, 17, 45, 92, 99, 76, 27, 7;
		

Links

• Heinrich Ludwig, Table of n, a(n) for n = 1..130
• Wikipedia, Fairy chess piece

Crossrefs

Cf. A008805, A232567, A278682, A278683, A278684, A278685, A278686, (columns 2 through 8 of this sequence, respectively), A278687, A093005 (row length - 1).