A194490 Number of ways to arrange 6 nonattacking knights on the lower triangle of an n X n board

0, 0, 0, 1, 230, 4257, 44005, 312296, 1693828, 7449231, 27785786, 90732814, 265594944, 709634275, 1755164932, 4063548824, 8885486966, 18484419808, 36802865115, 70481362597, 130377759323, 233782433461, 407584477894

Offset

1,5

Comments

Column 6 of A194492

Links

R. H. Hardin, Table of n, a(n) for n = 1..42

Formula

Empirical: a(n) = (1/46080)*n^12 + (1/7680)*n^11 - (17/3072)*n^10 - (13/4608)*n^9 + (6635/9216)*n^8 - (66667/23040)*n^7 - (2096789/46080)*n^6 + (1744105/4608)*n^5 + (10251671/11520)*n^4 - (107575289/5760)*n^3 + (46056797/1440)*n^2 + (984185/3)*n - 1221248 for n>13

Example

Some solutions for 5X5
..1..........1..........1..........0..........0..........0..........1
..0.0........0.0........1.0........0.0........1.1........0.0........0.1
..1.0.0......1.0.0......0.0.0......1.0.1......1.0.0......1.0.0......0.0.0
..0.0.0.1....1.0.0.1....1.0.0.0....0.0.0.1....0.0.0.1....0.0.0.1....0.0.0.1
..1.0.1.0.1..0.0.0.1.1..1.1.0.1.0..1.0.1.0.1..0.0.1.0.1..1.0.1.1.1..1.0.1.1.0

Crossrefs

Sequence in context: A251445 A251283 A251276 * A232379 A333136 A231061

Adjacent sequences: A194487 A194488 A194489 * A194491 A194492 A194493

Keyword

nonn

Author

R. H. Hardin Aug 26 2011

Status

approved