A227256 T(n,k)=Number of nXk binary arrays indicating whether each 2X2 subblock of a larger binary array has lexicographically nondecreasing rows and columns, for some larger (n+1)X(k+1) binary array with rows and columns of the latter in lexicographically nondecreasing order

1, 2, 2, 4, 3, 4, 7, 9, 9, 7, 11, 23, 36, 23, 11, 16, 53, 134, 134, 53, 16, 22, 113, 450, 813, 450, 113, 22, 29, 225, 1353, 4578, 4578, 1353, 225, 29, 37, 421, 3722, 22659, 44379, 22659, 3722, 421, 37, 46, 745, 9529, 98821, 385212, 385212, 98821, 9529, 745, 46, 56

Offset

1,2

Comments

Table starts

..1...2.....4.......7........11..........16...........22.............29

..2...3.....9......23........53.........113..........225............421

..4...9....36.....134.......450........1353.........3722...........9529

..7..23...134.....813......4578.......22659........98821.........388681

.11..53...450....4578.....44379......385212......2925969.......19641271

.16.113..1353...22659....385212.....6022992.....82991987.....1003726635

.22.225..3722...98821...2925969....82991987...2110707595....47221491430

.29.421..9529..388681..19641271..1003726635..47221491430..1972236759492

.37.745.22957.1403516.118614860.10790290999.934320610037.72868867008677

Links

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

Formula

Empirical for column k:

k=1: a(n) = (1/2)*n^2 - (1/2)*n + 1

k=2: [polynomial of degree 5] for n>1

k=3: [polynomial of degree 11] for n>3

k=4: [polynomial of degree 23] for n>8

k=5: [polynomial of degree 47] for n>30

Example

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

Crossrefs

Column 1 is A000124(n-1)

Sequence in context: A353925 A157927 A374396 * A328774 A131816 A223541

Adjacent sequences: A227253 A227254 A227255 * A227257 A227258 A227259

Keyword

nonn,tabl

Author

R. H. Hardin Jul 04 2013

Status

approved