A201503 T(n,k)=Number of nXk 0..1 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other

2, 1, 1, 2, 2, 2, 1, 2, 2, 1, 2, 3, 6, 3, 2, 1, 3, 5, 5, 3, 1, 2, 4, 12, 8, 12, 4, 2, 1, 4, 8, 12, 12, 8, 4, 1, 2, 5, 20, 18, 40, 18, 20, 5, 2, 1, 5, 13, 24, 32, 32, 24, 13, 5, 1, 2, 6, 30, 33, 98, 58, 98, 33, 30, 6, 2, 1, 6, 18, 43, 73, 94, 94, 73, 43, 18, 6, 1, 2, 7, 42, 55, 204, 151, 338, 151, 204

Offset

1,1

Comments

Table starts

.2.1..2..1...2...1...2....1....2....1....2.....1.....2.....1.....2......1

.1.2..2..3...3...4...4....5....5....6....6.....7.....7.....8.....8......9

.2.2..6..5..12...8..20...13...30...18...42....25....56....32....72.....41

.1.3..5..8..12..18..24...33...43...55...69....86...104...126...150....177

.2.3.12.12..40..32..98...73..204..141..380...252...650...414..1042....649

.1.4..8.18..32..58..94..151..227..338..480...676...920..1242..1636...2137

.2.4.20.24..98..94.338..289..936..734.2234..1656..4770..3370..9344...6375

.1.5.13.33..73.151.289..526..910.1514.2430..3788..5744..8512.12346..17575

.2.5.30.43.204.227.936..910.3334.2934.9936..8150.25908.20094.60882..45207

.1.6.18.55.141.338.734.1514.2934.5448.9686.16660.27718.44916.70922.109583

Links

R. H. Hardin, Table of n, a(n) for n = 1..3037

Example

Some solutions for n=5 k=4
..0..0..0..1....0..0..0..1....0..0..1..1....0..0..0..0....0..0..0..0
..0..0..0..1....0..0..0..1....0..0..1..1....0..0..0..0....0..0..1..1
..0..0..1..1....0..0..0..1....0..0..1..1....0..0..1..1....0..0..1..1
..0..1..1..1....0..1..1..1....0..0..1..1....1..1..1..1....0..0..1..1
..0..1..1..1....1..1..1..1....0..0..1..1....1..1..1..1....1..1..1..1

Crossrefs

Column 2 is A004526(n+2)

Column 3 odd terms are A002378((n+1)/2)

Column 3 even terms are A000982((n+2)/2)

Column 4 is A001973

Column 5 even terms are A188183((n-2)/2)

Column 6 is A001977

Column 7 even terms are A188185((n-4)/2)

Column 8 is A001981

Column 10 is A183913

Column 12 is A183914

Column 14 is A183915

Column 16 is A183916

Sequence in context: A317989 A106032 A003646 * A112758 A029437 A227908

Adjacent sequences: A201500 A201501 A201502 * A201504 A201505 A201506

Keyword

nonn,tabl

Author

R. H. Hardin Dec 02 2011

Status

approved