A227333 T(n,k) = Number of n X k 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X (k+1) binary array having two adjacent 1's and two adjacent 0's, with rows and columns of the latter in lexicographically nondecreasing order.

2, 4, 4, 8, 11, 8, 15, 34, 34, 15, 26, 104, 153, 104, 26, 42, 285, 708, 708, 285, 42, 64, 683, 3013, 4917, 3013, 683, 64, 93, 1469, 11292, 33297, 33297, 11292, 1469, 93, 130, 2906, 37312, 204206, 366606, 204206, 37312, 2906, 130, 176, 5383, 110816, 1108382

Offset

1,1

Comments

Table starts

...2....4......8.......15.........26..........42..........64..........93

...4...11.....34......104........285.........683........1469........2906

...8...34....153......708.......3013.......11292.......37312......110816

..15..104....708.....4917......33297......204206.....1108382.....5361624

..26..285...3013....33297.....366606.....3774137....35026386...290742258

..42..683..11292...204206....3774137....66730314..1084271645.15918049450

..64.1469..37312..1108382...35026386..1084271645.31357593706

..93.2906.110816..5361624..290742258.15918049450

.130.5383.301923.23477312.2174611745

Links

R. H. Hardin, Table of n, a(n) for n = 1..97

Formula

Empirical for column k:

k=1: a(n) = (1/6)*n^3 + (5/6)*n + 1.

k=2: [polynomial of degree 7] for n>2.

k=3: [polynomial of degree 15] for n>6.

k=4: [polynomial of degree 31] for n>10.

Example

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

Crossrefs

Column 1 is A000125.

Sequence in context: A265204 A073420 A034408 * A223317 A027131 A338986

Adjacent sequences: A227330 A227331 A227332 * A227334 A227335 A227336

Keyword

nonn,tabl

Author

R. H. Hardin Jul 07 2013

Status

approved