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A186915
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T(n,k)=Number of (n+2)X(k+2) 0..6 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order
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10
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2066505, 59969593, 59969593, 1276581035, 2974946682, 1276581035, 22000126445, 99241308567, 99241308567, 22000126445, 319741716426, 2536761070723, 4813465754996, 2536761070723, 319741716426, 4028133387613, 52666517720011
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OFFSET
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1,1
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COMMENTS
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Table starts
...........2066505.............59969593.............1276581035
..........59969593...........2974946682............99241308567
........1276581035..........99241308567..........4813465754996
.......22000126445........2536761070723........171334955820947
......319741716426.......52666517720011.......4805827783188400
.....4028133387613......921058887545363.....110909004238159456
....44902749582723....13921822487031205....2169936652932512523
...449959668016830...185414592506642580...36804096662464163093
..4103914508092780..2208956268019713255..550615265988952206164
.34409633745323847.23828517723857362267.7367827886026471340866
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LINKS
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FORMULA
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Empirical: T(n,k) is a polynomial of degree 6k+77, for fixed k.
Let T(n,k,z) be the number of (n+2)X(k+2) 0..z arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.
Then empirically T(n,k,z) is a polynomial of degree z*k + z*(z+1)*(z+5)/6 in n, for fixed k.
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EXAMPLE
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Some solutions for 5X4
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..1..1..3..3....1..1..1..5....0..1..4..6....0..1..5..6....1..2..4..4
..1..4..5..5....5..5..5..6....0..3..2..5....1..5..6..0....5..6..0..1
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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