A180983 T(n,k)=number of nXk binary matrices with floor((n*k)/2) 1's and rows in lexicographically nondecreasing order and columns in strictly increasing order

1, 1, 1, 0, 2, 1, 0, 1, 4, 1, 0, 1, 6, 6, 1, 0, 0, 10, 20, 9, 1, 0, 0, 9, 71, 49, 12, 1, 0, 0, 6, 200, 368, 109, 16, 1, 0, 0, 3, 450, 2403, 1502, 222, 20, 1, 0, 0, 1, 780, 13059, 19929, 5208, 412, 25, 1, 0, 0, 0, 1042, 60488, 238535, 135984, 15983, 712, 30, 1, 0, 0, 0, 1084

Offset

1,5

Comments

Table starts

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

.1..2....1......1........0..........0............0..............0

.1..4....6.....10........9..........6............3..............1

.1..6...20.....71......200........450..........780...........1042

.1..9...49....368.....2403......13059........60488.........221320

.1.12..109...1502....19929.....238535......2448773.......21398553

.1.16..222...5208...135984....3267300.....73506103.....1350956543

.1.20..412..15983...755144...36506260...1632383886....64732546521

.1.25..712..44485..3831820..348892547..32320317217..2541063599189

.1.30.1177.114320.16788240.2938265005.519815199311.85375670050862

Links

R. H. Hardin, Table of n, a(n) for n=1..199

Example

All solutions for 3X4
..0..0..0..1....0..0..0..1....0..0..0..1....0..0..1..1....0..0..1..1
..0..0..1..1....0..1..1..0....0..1..1..1....0..0..1..1....0..1..0..1
..0..1..1..1....1..0..1..1....1..0..1..0....0..1..0..1....0..1..1..0
...
..0..0..1..1....0..0..1..1....0..0..1..1....0..0..1..1....0..0..1..1
..0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..0....0..1..0..1
..0..1..0..1....1..0..1..0....1..0..0..1....1..1..0..1....1..1..0..0

Crossrefs

Sequence in context: A109970 A116088 A136501 * A127709 A343730 A343761

Adjacent sequences: A180980 A180981 A180982 * A180984 A180985 A180986

Keyword

nonn,tabl

Author

R. H. Hardin Sep 30 2010

Status

approved