A266362 T(n,k) = Number of n X k binary arrays with rows and columns lexicographically nondecreasing and row and column sums nondecreasing.

2, 3, 3, 4, 7, 4, 5, 13, 13, 5, 6, 22, 35, 22, 6, 7, 34, 82, 82, 34, 7, 8, 50, 173, 276, 173, 50, 8, 9, 70, 337, 830, 830, 337, 70, 9, 10, 95, 614, 2278, 3669, 2278, 614, 95, 10, 11, 125, 1060, 5752, 14921, 14921, 5752, 1060, 125, 11, 12, 161, 1749, 13525, 55734, 93085

Offset

1,1

Comments

Table starts

..2...3....4.....5.......6........7..........8..........9.........10.........11

..3...7...13....22......34.......50.........70.........95........125........161

..4..13...35....82.....173......337........614.......1060.......1749.......2777

..5..22...82...276.....830.....2278.......5752......13525......29864......62455

..6..34..173...830....3669....14921......55734.....191916.....612871....1827072

..7..50..337..2278...14921....93085.....541207....2909244...14424728...66153106

..8..70..614..5752...55734...541207....5061414...44435916..361401441.2711340372

..9..95.1060.13525..191916..2909244...44435916..654427939.9043864160

.10.125.1749.29864..612871.14424728..361401441.9043864160

.11.161.2777.62455.1827072.66153106.2711340372

Links

R. H. Hardin, Table of n, a(n) for n = 1..143

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) -a(n-2);

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

k=3: a(n) = 5*a(n-1) -9*a(n-2) +6*a(n-3) -6*a(n-7) +9*a(n-8) -5*a(n-9) +a(n-10).

Example

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

Crossrefs

Column 1 is A000027(n+1).

Column 2 is A002623.

Sequence in context: A361644 A185738 A239361 * A241956 A227125 A248944

Adjacent sequences: A266359 A266360 A266361 * A266363 A266364 A266365

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 28 2015

Status

approved