A180979 T(n,k)=number of nXk binary matrices with floor((n*k)/2) 1's and rows and columns in lexicographically nondecreasing order

1, 1, 1, 1, 3, 1, 1, 4, 4, 1, 1, 7, 10, 7, 1, 1, 9, 27, 27, 9, 1, 1, 13, 58, 121, 58, 13, 1, 1, 16, 122, 483, 483, 122, 16, 1, 1, 21, 238, 1751, 3680, 1751, 238, 21, 1, 1, 25, 433, 5694, 24779, 24779, 5694, 433, 25, 1, 1, 31, 737, 16870, 152453, 326650, 152453, 16870, 737

Offset

1,5

Comments

Table starts

.1..1....1......1........1..........1............1..............1

.1..3....4......7........9.........13...........16.............21

.1..4...10.....27.......58........122..........238............433

.1..7...27....121......483.......1751.........5694..........16870

.1..9...58....483.....3680......24779.......152453.........804538

.1.13..122...1751....24779.....326650......3826202.......39589830

.1.16..238...5694...152453....3826202.....91271990.....1819250859

.1.21..433..16870...804538...39589830...1819250859....74872992399

.1.25..737..46014..3969107..364013320..34112520431..2730227923892

.1.31.1208.116842.17135660.3005372641.534428405524.88478723671041

Links

R. H. Hardin, Table of n, a(n) for n=1..220

Example

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

Crossrefs

Sequence in context: A026747 A026374 A174032 * A102716 A173076 A134510

Adjacent sequences: A180976 A180977 A180978 * A180980 A180981 A180982

Keyword

nonn,tabl

Author

R. H. Hardin Sep 30 2010

Status

approved