

A243716


Irregular triangle read by rows: T(n, k) = number of inequivalent (mod the dihedral group D_8 of order 8) ways to place k nonattacking knights on an n X n board.


6



1, 1, 2, 1, 1, 3, 7, 9, 6, 2, 3, 18, 40, 66, 49, 30, 8, 3, 6, 43, 195, 609, 1244, 1767, 1710, 1148, 510, 154, 31, 6, 1, 6, 83, 618, 3375, 12329, 32524, 61731, 86748, 90059, 70128, 40770, 18053, 6089, 1643, 344, 61, 7, 1, 10, 156, 1751, 14181, 81900, 348541
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OFFSET

1,3


COMMENTS

The triangle is irregularly shaped: 1 <= k <= A030978(n). A030978(n) is the maximal number of knights that can be placed on an n X n board.
First row corresponds to n = 1.
Counting "inequivalent ways" means: Rotations or reflections of a placement of knights on the board are considered to be the same placement.


LINKS



EXAMPLE

The triangle begins:
1;
1, 2, 1, 1;
3, 7, 9, 6, 2;
3, 18, 40, 66, 49, 30, 8, 3;
6, 43, 195, 609, 1244, 1767, 1710, 1148, 510, 154, 31, 6, 1;
...


CROSSREFS



KEYWORD

nonn,tabf


AUTHOR



STATUS

approved



