A194489 Number of ways to arrange 5 nonattacking knights on the lower triangle of an n X n board

0, 0, 0, 13, 387, 3727, 23496, 111433, 429343, 1407755, 4061432, 10561723, 25208796, 55996244, 117021864, 232070481, 439779278, 800893832, 1408234986, 2400123737, 3978154435, 6430366713, 10161044648, 15728568633, 23892962265, 35675014169

Offset

1,4

Comments

Column 5 of A194492

Links

R. H. Hardin, Table of n, a(n) for n = 1..68

Formula

Empirical: a(n) = (1/3840)*n^10 + (1/768)*n^9 - (17/384)*n^8 + (3/128)*n^7 + (951/256)*n^6 - (68939/3840)*n^5 - (1433/12)*n^4 + (230047/192)*n^3 - (149581/240)*n^2 - (718267/30)*n + 72425 for n>10

Example

Some solutions for 4X4
..1........1........0........0........1........1........1........1
..0.0......0.1......0.1......0.1......1.1......1.0......0.0......0.0
..1.0.1....1.0.1....1.0.1....1.1.1....1.0.0....0.0.0....0.0.0....0.0.1
..0.1.0.1..0.1.0.0..0.1.0.1..0.1.0.0..0.0.0.1..1.0.1.1..1.1.1.1..0.1.1.1

Crossrefs

Sequence in context: A142122 A370379 A302700 * A354138 A356740 A275651

Adjacent sequences: A194486 A194487 A194488 * A194490 A194491 A194492

Keyword

nonn

Author

R. H. Hardin Aug 26 2011

Status

approved