A194488 Number of ways to arrange 4 nonattacking knights on the lower triangle of an n X n board

0, 0, 4, 46, 407, 2168, 8685, 28376, 79611, 198334, 449336, 942072, 1852096, 3449261, 6133944, 10482661, 17304542, 27710241, 43194961, 65737379, 97916361, 143047462, 205341311, 290086086, 403856389, 554750936, 752661582, 1009576306, 1339918886

Offset

1,3

Comments

Column 4 of A194492

Links

R. H. Hardin, Table of n, a(n) for n = 1..117

Formula

Empirical: a(n) = (1/384)*n^8 + (1/96)*n^7 - (17/64)*n^6 + (5/12)*n^5 + (1571/128)*n^4 - (6653/96)*n^3 - (8641/96)*n^2 + (13951/8)*n - 4161 for n>7

Example

Some solutions for 4X4
..1........1........1........1........1........1........1........0
..0.0......1.1......1.0......1.1......0.0......0.0......0.0......1.0
..1.0.0....1.0.0....0.0.0....0.0.0....0.0.0....0.0.0....0.0.0....0.0.0
..0.1.0.1..0.0.0.0..0.0.1.1..0.0.0.1..1.1.0.1..1.0.1.1..0.1.1.1..1.0.1.1

Crossrefs

Sequence in context: A131540 A218997 A279523 * A132932 A231787 A173716

Adjacent sequences: A194485 A194486 A194487 * A194489 A194490 A194491

Keyword

nonn

Author

R. H. Hardin Aug 26 2011

Status

approved