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A224353
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T(n,k)=Number of nXk 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing
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12
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3, 6, 9, 10, 36, 27, 15, 100, 216, 81, 21, 225, 788, 1296, 243, 28, 441, 2321, 5880, 7776, 729, 36, 784, 5840, 19608, 45064, 46656, 2187, 45, 1296, 13052, 57387, 160362, 349280, 279936, 6561, 55, 2025, 26610, 151010, 495985, 1351748, 2710892, 1679616
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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.......36........100........225.........441.........784.........1296
....27......216........788.......2321........5840.......13052........26610
....81.....1296.......5880......19608.......57387......151010.......363392
...243.....7776......45064.....160362......495985.....1421762......3816783
...729....46656.....349280....1351748.....4231138....12340932.....34697869
..2187...279936....2710892...11704964....37433596...107694133....300892325
..6561..1679616...21021916..102319662...342170839...977742699...2654062881
.19683.10077696..163012744..895494806..3178789749..9202126546..24422915139
.59049.60466176.1264202660.7833508842.29672959682.88363107023.233364588801
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LINKS
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FORMULA
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Empirical: columns k=1..6 have recurrences of order 1,1,10,26,56,98
Empirical: rows n=1..7 are polynomials of degree 2*n for k>0,0,1,3,5,7,9
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EXAMPLE
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Some solutions for n=3 k=4
..1..1..1..2....0..0..1..1....0..0..2..2....1..2..2..2....0..2..2..2
..1..1..1..2....0..0..2..2....0..1..1..2....0..1..2..2....1..1..2..2
..0..0..1..2....0..1..1..1....0..1..1..2....1..2..2..2....1..1..1..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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