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.

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

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

Heinrich Ludwig, Table of n, a(n) for n = 1..116

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

Cf. A030978, A008805 (column 1), A243717 (column 2), A243718 (column 3), A243719 (column 4), A243720 (column 5).

Sequence in context: A361707 A135701 A051467 * A356776 A333988 A195805

Adjacent sequences: A243713 A243714 A243715 * A243717 A243718 A243719

Keyword

nonn,tabf

Author

Heinrich Ludwig, Jun 10 2014

Status

approved