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A223999
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T(n,k)=Number of nXk 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing
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13
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3, 6, 9, 10, 31, 27, 15, 76, 157, 81, 21, 155, 476, 793, 243, 28, 281, 1144, 2980, 4004, 729, 36, 469, 2403, 7927, 18672, 20216, 2187, 45, 736, 4614, 17929, 55333, 117386, 102069, 6561, 55, 1101, 8291, 36845, 132119, 388598, 739672, 515338, 19683, 66
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OFFSET
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1,1
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COMMENTS
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Table starts
.....3........6........10........15.........21.........28..........36
.....9.......31........76.......155........281........469.........736
....27......157.......476......1144.......2403.......4614........8291
....81......793......2980......7927......17929......36845.......71061
...243.....4004.....18672.....55333.....132119.....281271......559188
...729....20216....117386....388598.....984595....2160036.....4368458
..2187...102069....739672...2743444....7400832...16795265....34534687
..6561...515338...4664776..19437479...55978489..131782267...276286000
.19683..2601899..29428242.138010718..425257387.1040869367..2229871293
.59049.13136773.185670484.981047716.3240026429.8260503068.18115082917
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LINKS
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FORMULA
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Empirical: columns k=1..7 have recurrences of order 1,3,9,18,28,39,54 for n>0,0,0,19,31,44,61
Empirical: rows n=1..7 are polynomials of degree 2*n for k>0,0,2,4,6,8,10
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EXAMPLE
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Some solutions for n=3 k=4
..0..0..0..1....1..1..2..2....0..0..0..0....2..2..2..2....0..0..0..0
..0..1..2..2....0..1..1..2....0..0..2..2....0..2..2..2....0..0..2..2
..2..2..2..2....0..0..1..2....0..0..1..2....2..2..2..2....2..2..2..2
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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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