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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.

%I A278688 #15 Nov 30 2016 13:03:38
%S A278688 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 A278688 3773,4860,4643,3356,1868,795,248,56,8,1,1,6,84,709,4500,19987,66201,
%U A278688 164423,314224,465230,540247,492206,352300,195717,83247,26083,5754,780,55
%N 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.
%C A278688 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 A278688 Two placements that differ by rotation or reflection are counted only once.
%C A278688 A fers is a fairy chess piece attacking one step ne-nw-sw-se.
%H A278688 Heinrich Ludwig, <a href="/A278688/b278688.txt">Table of n, a(n) for n = 1..130</a>
%H A278688 Wikipedia, <a href="http://en.wikipedia.org/wiki/Fairy_chess_piece">Fairy chess piece</a>
%e A278688 Triangle begins:
%e A278688 1, 1;
%e A278688 1, 1,  1;
%e A278688 1, 3,  6,  7,  6,  2,  1;
%e A278688 1, 3, 17, 45, 92, 99, 76, 27, 7;
%Y A278688 Cf. A008805, A232567, A278682, A278683, A278684, A278685, A278686, (columns 2 through 8 of this sequence, respectively), A278687, A093005 (row length - 1).
%K A278688 nonn,tabf
%O A278688 1,7
%A A278688 _Heinrich Ludwig_, Nov 27 2016