A266935 T(n,k)=Number of nXk binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

2, 2, 3, 2, 4, 4, 2, 4, 7, 5, 2, 5, 9, 12, 6, 2, 5, 12, 20, 19, 7, 2, 6, 14, 35, 44, 29, 8, 2, 6, 19, 52, 100, 92, 42, 9, 2, 7, 21, 82, 210, 288, 182, 59, 10, 2, 7, 26, 115, 429, 871, 794, 340, 80, 11, 2, 8, 30, 169, 816, 2577, 3566, 2077, 605, 106, 12, 2, 8, 35, 232, 1534, 7185

Offset

1,1

Comments

Table starts

..2...2....2.....2......2.......2........2..........2.........2.........2

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

..4...7....9....12.....14......19.......21.........26........30........35

..5..12...20....35.....52......82......115........169.......232.......322

..6..19...44...100....210.....429......816.......1534......2727......4753

..7..29...92...288....871....2577.....7185......19529.....50216....125786

..8..42..182...794...3566...15850....68890.....288333...1155281...4410923

..9..59..340..2077..13899...96503...671796....4605960..30319512.191420936

.10..80..605..5110..50841..555060..6347005...73046059.821453747

.11.106.1028.11869.173470.2977370.56180274.1104862960

Links

R. H. Hardin, Table of n, a(n) for n = 1..160

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: [order 11]

k=4: [order 31]

Empirical for row n:

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

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

n=3: a(n) = a(n-1) +a(n-2) -a(n-4) -a(n-5) +a(n-6)

n=4: [order 17]

Example

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

Crossrefs

Column 1 is A000027(n+1).

Column 2 is A266464.

Row 2 is A004526(n+6).

Sequence in context: A218700 A325331 A333108 * A175012 A051693 A266470

Adjacent sequences: A266932 A266933 A266934 * A266936 A266937 A266938

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 06 2016

Status

approved