A194498 T(n,k)=Number of ways to arrange k nonattacking queens on the lower triangle of an n X n board.

1, 0, 3, 0, 0, 6, 0, 0, 2, 10, 0, 0, 0, 12, 15, 0, 0, 0, 0, 38, 21, 0, 0, 0, 0, 12, 92, 28, 0, 0, 0, 0, 0, 82, 188, 36, 0, 0, 0, 0, 0, 8, 330, 344, 45, 0, 0, 0, 0, 0, 0, 118, 1008, 580, 55, 0, 0, 0, 0, 0, 0, 4, 802, 2566, 920, 66, 0, 0, 0, 0, 0, 0, 0, 114, 3708, 5742, 1390, 78, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

R. H. Hardin Aug 26 2011

Keywords

• nonn
• tabl

Comments

Table starts

...1....0......0.......0........0........0........0........0........0......0..0

...3....0......0.......0........0........0........0........0........0......0..0

...6....2......0.......0........0........0........0........0........0......0..0

..10...12......0.......0........0........0........0........0........0......0..0

..15...38.....12.......0........0........0........0........0........0......0..0

..21...92.....82.......8........0........0........0........0........0......0..0

..28..188....330.....118........4........0........0........0........0......0..0

..36..344...1008.....802......114........0........0........0........0......0..0

..45..580...2566....3708.....1384.......64........0........0........0......0..0

..55..920...5742...13280.....9890.....1644.......10........0........0......0..0

..66.1390..11652...39734....50662....19306.....1210........0........0......0..0

..78.2020..21926..104000...205512...146718....27198......484........0......0..0

..91.2842..38802..244948...698688...820218...322782....26084.......38......0..0

.105.3892..65322..530632..2074530..3670288..2564988...531344....14870......0..0

.120.5208.105428.1072776..5525902.13846830.15372702..6285270...629414...3656..0

.136.6832.164214.2048056.13476246.45661556.74615814.51834064.11949712.501700.56

Examples

			Some solutions for n=6 k=4
..0............0............0............0............0............0
..0.0..........0.0..........0.1..........0.0..........1.0..........0.1
..1.0.0........1.0.0........0.0.0........0.0.1........0.0.1........0.0.0
..0.0.1.0......0.0.0.1......0.0.1.0......1.0.0.0......0.0.0.0......1.0.0.0
..0.0.0.0.1....0.1.0.0.0....1.0.0.0.0....0.0.0.1.0....0.1.0.0.0....0.0.1.0.0
..0.1.0.0.0.0..0.0.0.0.1.0..0.0.0.1.0.0..0.1.0.0.0.0..0.0.0.1.0.0..0.0.0.0.1.0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..518

Crossrefs

Column 1 is A000217

Column 2 is 2*A070893(n-2)