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

1,3

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

Links

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

Example

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

Crossrefs

Column 1 is A000217

Column 2 is 2*A070893(n-2)

Sequence in context: A362021 A330735 A127773 * A193986 A376203 A062688

Adjacent sequences: A194495 A194496 A194497 * A194499 A194500 A194501

Keyword

nonn,tabl

Author

R. H. Hardin Aug 26 2011

Status

approved