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A227385
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
5
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, 587, 98, 8, 9, 162, 1704, 6160, 6160, 1704, 162, 9, 10, 255, 4532, 31073, 61127, 31073, 4532, 255, 10, 11, 385, 11126, 141192, 550010, 550010, 141192, 11126, 385, 11, 12, 561
OFFSET
1,1
COMMENTS
Table starts
..2...3.....4.......5.........6...........7...........8...........9..........10
..3...7....15......30........56..........98.........162.........255.........385
..4..15....54.....185.......587........1704........4532.......11126.......25430
..5..30...185....1104......6160.......31073......141192......581706.....2192737
..6..56...587....6160.....61127......550010.....4450124....32473856...215116595
..7..98..1704...31073....550010.....8988949...133142369..1779353333.21501389691
..8.162..4532..141192...4450124...133142369..3657501287.91016881301
..9.255.11126..581706..32473856..1779353333.91016881301
.10.385.25430.2192737.215116595.21501389691
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = n + 1
k=2: a(n) = (1/24)*n^4 + (1/12)*n^3 + (11/24)*n^2 + (17/12)*n + 1
k=3: [polynomial of degree 9] for n>3
k=4: [polynomial of degree 19] for n>7
k=5: [polynomial of degree 39] for n>22
EXAMPLE
Some solutions for n=4 k=4
..1..0..0..0....0..0..0..1....1..0..0..0....0..0..1..0....0..0..1..0
..0..0..1..0....1..0..0..0....0..0..1..0....0..1..0..1....0..1..0..0
..0..0..1..1....0..0..0..0....0..0..1..0....1..0..1..1....1..0..1..0
..0..0..1..1....0..0..0..1....0..0..0..0....0..1..0..1....0..1..1..1
CROSSREFS
Column 2 is A055795(n+2)
Sequence in context: A267245 A266428 A180985 * A049790 A222188 A368307
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Jul 09 2013
STATUS
approved