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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 6
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 (list; table; graph; refs; listen; history; text; internal format)
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: A178431 A233574 A157927 * A328774 A131816 A223541

Adjacent sequences:  A227253 A227254 A227255 * A227257 A227258 A227259

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Jul 04 2013

STATUS

approved

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Last modified July 24 14:45 EDT 2021. Contains 346273 sequences. (Running on oeis4.)