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T(n,k)=Number of nXk 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X(k+1) binary array having a sum of one, with rows and columns of the latter in lexicographically nondecreasing order
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%I #4 Jul 09 2013 13:23:51

%S 2,3,3,4,7,4,5,15,15,5,6,30,54,30,6,7,56,185,185,56,7,8,98,587,1104,

%T 587,98,8,9,162,1704,6160,6160,1704,162,9,10,255,4532,31073,61127,

%U 31073,4532,255,10,11,385,11126,141192,550010,550010,141192,11126,385,11,12,561

%N T(n,k)=Number of nXk 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X(k+1) binary array having a sum of one, with rows and columns of the latter in lexicographically nondecreasing order

%C Table starts

%C ..2...3.....4.......5.........6...........7...........8...........9..........10

%C ..3...7....15......30........56..........98.........162.........255.........385

%C ..4..15....54.....185.......587........1704........4532.......11126.......25430

%C ..5..30...185....1104......6160.......31073......141192......581706.....2192737

%C ..6..56...587....6160.....61127......550010.....4450124....32473856...215116595

%C ..7..98..1704...31073....550010.....8988949...133142369..1779353333.21501389691

%C ..8.162..4532..141192...4450124...133142369..3657501287.91016881301

%C ..9.255.11126..581706..32473856..1779353333.91016881301

%C .10.385.25430.2192737.215116595.21501389691

%H R. H. Hardin, <a href="/A227385/b227385.txt">Table of n, a(n) for n = 1..111</a>

%F Empirical for column k:

%F k=1: a(n) = n + 1

%F k=2: a(n) = (1/24)*n^4 + (1/12)*n^3 + (11/24)*n^2 + (17/12)*n + 1

%F k=3: [polynomial of degree 9] for n>3

%F k=4: [polynomial of degree 19] for n>7

%F k=5: [polynomial of degree 39] for n>22

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 2 is A055795(n+2)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Jul 09 2013