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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

%I

%S 1,2,2,4,3,4,7,9,9,7,11,23,36,23,11,16,53,134,134,53,16,22,113,450,

%T 813,450,113,22,29,225,1353,4578,4578,1353,225,29,37,421,3722,22659,

%U 44379,22659,3722,421,37,46,745,9529,98821,385212,385212,98821,9529,745,46,56

%N 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

%C Table starts

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

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

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

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

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

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

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

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

%C .37.745.22957.1403516.118614860.10790290999.934320610037.72868867008677

%H R. H. Hardin, <a href="/A227256/b227256.txt">Table of n, a(n) for n = 1..143</a>

%F Empirical for column k:

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

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

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

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

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

%e Some solutions for n=4 k=4

%e ..1..1..0..0....1..1..1..1....1..1..0..1....1..1..1..1....1..1..1..1

%e ..1..0..1..1....1..1..0..0....1..0..1..1....1..1..0..0....1..1..0..0

%e ..1..0..1..0....1..0..0..1....1..0..0..0....1..0..1..1....1..0..0..0

%e ..0..1..1..1....0..1..1..0....0..0..1..1....0..1..0..0....1..0..0..1

%Y Column 1 is A000124(n-1)

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_ Jul 04 2013

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Last modified September 26 23:42 EDT 2021. Contains 347673 sequences. (Running on oeis4.)