A194491 Number of ways to arrange 7 nonattacking knights on the lower triangle of an n X n board

0, 0, 0, 0, 88, 3300, 58630, 641678, 5025711, 30209361, 147914590, 614046090, 2226985986, 7218141771, 21280624486, 57867863073, 146765501360, 350324696309, 792870137966, 1711961366458, 3544779914099, 7069433034465, 13630030399362

Offset

1,5

Comments

Column 7 of A194492

Links

R. H. Hardin, Table of n, a(n) for n = 1..35

Formula

Empirical: a(n) = (1/645120)*n^14 + (1/92160)*n^13 - (17/30720)*n^12 - (79/92160)*n^11 + (1047/10240)*n^10 - (29857/92160)*n^9 - (946249/92160)*n^8 + (48326573/645120)*n^7 + (7473253/15360)*n^6 - (153662159/23040)*n^5 - (1018307/768)*n^4 + (40217689/144)*n^3 - (212485407/280)*n^2 - (316047321/70)*n + 20362649 for n>16

Example

Some solutions for 5X5
..0..........1..........0..........1..........0..........0..........1
..1.1........0.1........1.0........0.0........0.1........1.1........1.0
..0.0.0......1.0.1......1.0.0......0.0.1......1.0.0......1.0.0......1.0.0
..0.0.0.0....0.1.0.1....1.0.0.1....0.1.0.1....0.0.0.1....0.0.0.1....0.0.0.1
..1.1.1.1.1..0.0.0.0.1..1.0.0.1.1..1.0.1.0.1..1.0.1.1.1..1.0.1.1.0..1.0.0.1.1

Crossrefs

Sequence in context: A248047 A107422 A210006 * A093288 A017804 A035739

Adjacent sequences: A194488 A194489 A194490 * A194492 A194493 A194494

Keyword

nonn

Author

R. H. Hardin Aug 26 2011

Status

approved