A194493 Number of ways to arrange 3 nonattacking queens on the lower triangle of an n X n board

0, 0, 0, 0, 12, 82, 330, 1008, 2566, 5742, 11652, 21926, 38802, 65322, 105428, 164214, 248022, 364764, 523998, 737334, 1018488, 1383768, 1852104, 2445628, 3189660, 4113396, 5249848, 6636636, 8315880, 10335110, 12747090, 15610860, 18991490

Offset

1,5

Comments

Column 3 of A194498

Links

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

Formula

Empirical: a(n) = 3*a(n-1) -7*a(n-3) +3*a(n-4) +6*a(n-5) -6*a(n-7) -3*a(n-8) +7*a(n-9) -3*a(n-11) +a(n-12), [R. H. Hardin Aug 26 2011]

G.f.: -2*x^5*(18*x^5 + 40*x^4 + 51*x^3 + 42*x^2 + 23*x + 6)/((x-1)^7*(x+1)^3*(x^2+x+1))

Explicit formula: n^6/48 - 11*n^5/48 + 15*n^4/16 - 241*n^3/144 + 17*n^2/16 - 17*n/144 + (n^2/8 - 9*n/8 + 17/8)*floor(n/2) + 2/3*floor(n/3), [Vaclav Kotesovec, Apr 08 2012]

Example

Some solutions for 5X5
..0..........0..........0..........0..........0..........0..........1
..1.0........0.1........1.0........0.0........1.0........0.1........0.0
..0.0.0......0.0.0......0.0.0......1.0.0......0.0.1......0.0.0......0.1.0
..0.1.0.0....1.0.0.0....0.0.0.1....0.0.0.1....0.0.0.0....1.0.0.0....0.0.0.0
..0.0.0.0.1..0.0.1.0.0..0.1.0.0.0..0.1.0.0.0..0.1.0.0.0..0.0.0.1.0..0.0.1.0.0

Crossrefs

Sequence in context: A007010 A069996 A183504 * A163020 A164300 A239180

Adjacent sequences: A194490 A194491 A194492 * A194494 A194495 A194496

Keyword

nonn

Author

R. H. Hardin Aug 26 2011

Status

approved