A266547 T(n,k)=Number of nXk binary arrays with rows and columns lexicographically nondecreasing and row and column sums nonincreasing.

2, 2, 2, 2, 3, 2, 2, 3, 3, 2, 2, 4, 5, 4, 2, 2, 4, 6, 6, 4, 2, 2, 5, 8, 12, 8, 5, 2, 2, 5, 11, 16, 16, 11, 5, 2, 2, 6, 13, 27, 36, 27, 13, 6, 2, 2, 6, 16, 36, 58, 58, 36, 16, 6, 2, 2, 7, 20, 57, 110, 176, 110, 57, 20, 7, 2, 2, 7, 23, 76, 196, 366, 366, 196, 76, 23, 7, 2, 2, 8, 27, 114, 363

Offset

1,1

Comments

Table starts

.2.2..2...2...2....2......2.......2........2........2........2........2.......2

.2.3..3...4...4....5......5.......6........6........7........7........8.......8

.2.3..5...6...8...11.....13......16.......20.......23.......27.......32......36

.2.4..6..12..16...27.....36......57.......76......114......149......213.....276

.2.4..8..16..36...58....110.....196......363......695.....1157.....2023....3446

.2.5.11..27..58..176....366....1062.....2571.....7345....17540....47970..109375

.2.5.13..36.110..366...1688....5312....24921...101495...417118..1673507.6081357

.2.6.16..57.196.1062...5312...48167...264355..2251914.13562215.97760446

.2.6.20..76.363.2571..24921..264355..4283651.40874990

.2.7.23.114.695.7345.101495.2251914.40874990

Links

R. H. Hardin, Table of n, a(n) for n = 1..179

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = a(n-1) +a(n-2) -a(n-3)

k=3: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -2*a(n-4) +a(n-5)

k=4: [order 17]

Example

Some solutions for n=6 k=4
..0..0..1..1....0..0..1..1....0..0..0..1....0..0..1..1....0..0..1..1
..0..1..0..1....0..1..0..0....0..0..1..0....0..0..1..1....0..0..1..1
..1..0..1..0....1..0..0..0....0..1..0..0....0..0..1..1....1..1..0..0
..1..1..0..0....1..0..0..0....0..1..0..0....1..1..0..0....1..1..0..0
..1..1..0..0....1..0..0..0....1..0..0..0....1..1..0..0....1..1..0..0
..1..1..0..0....1..0..0..0....1..0..0..0....1..1..0..0....1..1..0..0

Crossrefs

Column 2 is A004526(n+4).

Sequence in context: A270966 A138139 A259578 * A127992 A327390 A169989

Adjacent sequences: A266544 A266545 A266546 * A266548 A266549 A266550

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 31 2015

Status

approved