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A224158
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T(n,k)=Number of nXk 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing
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12
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2, 4, 4, 7, 12, 8, 11, 28, 36, 16, 16, 56, 89, 108, 32, 22, 101, 187, 281, 324, 64, 29, 169, 373, 574, 900, 972, 128, 37, 267, 702, 1156, 1783, 2935, 2916, 256, 46, 403, 1252, 2271, 3469, 5657, 9681, 8748, 512, 56, 586, 2130, 4339, 6786, 10562, 18408, 32020, 26244
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OFFSET
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1,1
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COMMENTS
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Table starts
....2.....4......7.....11......16......22......29......37.......46.......56
....4....12.....28.....56.....101.....169.....267.....403......586......826
....8....36.....89....187.....373.....702....1252....2130.....3479.....5486
...16...108....281....574....1156....2271....4339....8008....14257....24519
...32...324....900...1783....3469....6786...13283...25624....48339....88755
...64...972...2935...5657...10562...20065...39037...76393...148637...284937
..128..2916...9681..18408...32910...60214..114537..222841...437497...857104
..256..8748..32020..61140..105020..184233..340134..650819..1271950..2506424
..512.26244.105937.205390..342575..575410.1025559.1918648..3705824..7278086
.1024.78732.350311.694018.1136503.1833641.3143071.5721195.10873402.21181267
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LINKS
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FORMULA
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Empirical: columns k=1..7 have recurrences of order 1,1,9,13,20,24,33 for n>0,0,0,14,22,27,37
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..0....1..1..0..0....0..0..1..0....0..1..1..0....0..0..1..0
..0..0..0..0....1..0..0..0....1..1..0..0....1..1..1..1....1..1..1..0
..0..0..1..0....0..0..0..0....1..1..1..0....1..1..1..1....1..1..1..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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