A194486 Number of ways to arrange 2 nonattacking knights on the lower triangle of an n X n board

0, 3, 13, 37, 87, 178, 328, 558, 892, 1357, 1983, 2803, 3853, 5172, 6802, 8788, 11178, 14023, 17377, 21297, 25843, 31078, 37068, 43882, 51592, 60273, 70003, 80863, 92937, 106312, 121078, 137328, 155158, 174667, 195957, 219133, 244303, 271578, 301072

Offset

1,2

Comments

Column 2 of A194492.

Links

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

Formula

Empirical: a(n) = (1/8)*n^4 + (1/4)*n^3 - (17/8)*n^2 + (31/4)*n - 8 for n>1.

Empirical g.f.: x^2*(3 - 2*x + 2*x^2 + 2*x^3 - 2*x^4) / (1 - x)^5. - Colin Barker, May 05 2018

Example

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

Crossrefs

Cf. A194492.

Sequence in context: A254955 A098547 A256316 * A024535 A196235 A120479

Adjacent sequences: A194483 A194484 A194485 * A194487 A194488 A194489

Keyword

nonn

Author

R. H. Hardin, Aug 26 2011

Status

approved