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A224374
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T(n,k)=Number of nXk 0..2 arrays with rows unimodal and antidiagonals nondecreasing
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12
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3, 9, 9, 22, 54, 27, 46, 218, 324, 81, 86, 698, 1838, 1944, 243, 148, 1915, 7608, 15540, 11664, 729, 239, 4690, 26314, 77793, 132236, 69984, 2187, 367, 10511, 80819, 311367, 800309, 1126072, 419904, 6561, 541, 21919, 227112, 1092281, 3607078, 8297747
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OFFSET
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1,1
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COMMENTS
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Table starts
.....3........9.........22..........46...........86...........148
.....9.......54........218.........698.........1915..........4690
....27......324.......1838........7608........26314.........80819
....81.....1944......15540.......77793.......311367.......1092281
...243....11664.....132236......800309......3607078......13831334
...729....69984....1126072.....8297747.....42132769.....174854516
..2187...419904....9588028....86251004....495660330....2231009824
..6561..2519424...81634704...896856330...5848449149...28645726612
.19683.15116544..695055928..9325161494..69064897862..368818252942
.59049.90699264.5917866680.96954549463.815702088065.4752723627808
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LINKS
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FORMULA
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Empirical: columns k=1..7 have recurrences of order 1,1,5,7,11,14,19 for n>0,0,0,8,13,18,24
Empirical: rows n=1..7 are polynomials of order 4*n for k>0,0,0,2,3,4,5
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EXAMPLE
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Some solutions for n=3 k=4
..2..2..2..2....0..0..1..2....1..2..0..0....1..2..1..1....1..1..2..0
..2..2..2..1....2..2..2..2....2..1..1..1....2..2..2..2....1..2..2..0
..2..2..2..1....2..2..2..2....2..2..1..1....2..2..2..0....2..2..1..1
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CROSSREFS
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Column 2 is 9*6^(n-1)
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KEYWORD
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AUTHOR
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STATUS
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approved
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