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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. 6
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 (list; table; graph; refs; listen; history; text; internal format)
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 A319803

Adjacent sequences:  A227330 A227331 A227332 * A227334 A227335 A227336

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Jul 07 2013

STATUS

approved

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Last modified October 31 19:00 EDT 2020. Contains 338111 sequences. (Running on oeis4.)