login
Triangle read by rows T(n, k) = number of non-equivalent ways to place k non-attacking ferses on an n X n board.
7

%I #15 Nov 30 2016 13:03:38

%S 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,

%T 3773,4860,4643,3356,1868,795,248,56,8,1,1,6,84,709,4500,19987,66201,

%U 164423,314224,465230,540247,492206,352300,195717,83247,26083,5754,780,55

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

%C 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.

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

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

%H Heinrich Ludwig, <a href="/A278688/b278688.txt">Table of n, a(n) for n = 1..130</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Fairy_chess_piece">Fairy chess piece</a>

%e Triangle begins:

%e 1, 1;

%e 1, 1, 1;

%e 1, 3, 6, 7, 6, 2, 1;

%e 1, 3, 17, 45, 92, 99, 76, 27, 7;

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

%K nonn,tabf

%O 1,7

%A _Heinrich Ludwig_, Nov 27 2016