A194487 Number of ways to arrange 3 nonattacking knights on the lower triangle of an n X n board.

0, 1, 12, 62, 253, 804, 2136, 4958, 10376, 20013, 36144, 61846, 101163, 159286, 242748, 359634, 519806, 735143, 1019796, 1390458, 1866649, 2471016, 3229648, 4172406, 5333268, 6750689, 8467976, 10533678, 13001991, 15933178, 19394004

Offset

1,3

Comments

Column 3 of A194492.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = (1/48)*n^6 + (1/16)*n^5 - (17/16)*n^4 + (133/48)*n^3 + (433/24)*n^2 - (743/6)*n + 218 for n>4.

Empirical g.f.: x^2*(1 + 5*x - x^2 + 36*x^3 - 50*x^4 + 50*x^5 - 40*x^6 + 22*x^7 - 12*x^8 + 4*x^9) / (1 - x)^7. - Colin Barker, May 05 2018

Example

Some solutions for 3 X 3:
..1......0......1......1......0......0......1......0......0......0......1
..0.1....1.1....1.1....1.0....0.1....0.1....0.1....1.0....1.1....0.0....0.0
..1.0.0..1.0.0..0.0.0..1.0.0..0.1.1..1.0.1..0.0.1..1.1.0..0.1.0..1.1.1..1.0.1

Crossrefs

Cf. A194492.

Sequence in context: A045822 A065595 A267472 * A196312 A196285 A196335

Adjacent sequences: A194484 A194485 A194486 * A194488 A194489 A194490

Keyword

nonn

Author

R. H. Hardin, Aug 26 2011

Status

approved