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A224310
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T(n,k)=Number of nXk 0..2 arrays with diagonals and 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, 1586, 1944, 243, 148, 1915, 5996, 11361, 11664, 729, 239, 4690, 20214, 45453, 82700, 69984, 2187, 367, 10511, 61953, 164514, 345875, 615481, 419904, 6561, 541, 21919, 174378, 562760, 1258372, 2717759
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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..........239
.....9.......54........218.........698........1915.........4690........10511
....27......324.......1586........5996.......20214........61953.......174378
....81.....1944......11361.......45453......164514.......562760......1825800
...243....11664......82700......345875.....1258372......4420701.....15312504
...729....69984.....615481.....2717759.....9829605.....33934344....118317987
..2187...419904....4634768....22071219....80083648....268379906....911404794
..6561..2519424...35003328...182843194...677557164...2215451575...7236130163
.19683.15116544..264487714..1528645389..5882182248..19023816444..59751261572
.59049.90699264.1997888432.12825738594.51821072499.168305254414.512310103541
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 3*a(n-1)
k=2: a(n) = 6*a(n-1)
k=3: [order 17]
k=4: [order 30] for n>35
k=5: [order 61] for n>69
k=6: [order 88] for n>98
Empirical: rows n=1..7 are polynomials of degree 4*n for k>0,0,3,6,9,12,15
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EXAMPLE
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Some solutions for n=3 k=4
..0..0..1..0....0..0..0..1....0..0..0..1....0..2..1..0....0..0..2..0
..1..2..1..0....0..1..1..0....0..0..1..0....2..1..1..0....2..2..2..0
..2..1..1..1....1..2..2..2....2..2..0..0....1..1..2..0....2..2..1..0
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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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