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A224409
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T(n,k)=Number of nXk 0..1 arrays with 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, 100, 108, 32, 22, 101, 228, 358, 324, 64, 29, 169, 465, 884, 1288, 972, 128, 37, 267, 879, 1928, 3436, 4636, 2916, 256, 46, 403, 1568, 3902, 7812, 13440, 16684, 8748, 512, 56, 586, 2668, 7490, 16420, 31710, 52700, 60040
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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
....4....12.....28......56.....101......169......267......403.......586
....8....36....100.....228.....465......879.....1568.....2668......4362
...16...108....358.....884....1928.....3902.....7490....13784.....24467
...32...324...1288....3436....7812....16420....32814....63202....118117
...64...972...4636...13440...31710....68282...139638...275766....530583
..128..2916..16684...52700..129402...284254...590254..1183226...2313915
..256..8748..60040..206708..529846..1187830..2496332..5055858...9988498
..512.26244.216064..810664.2172346..4979464.10583872.21606456..42996954
.1024.78732.777544.3178940.8908986.20913026.44986080.92478100.185065944
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LINKS
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FORMULA
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Empirical: columns k=1..7 have recurrences of order 1,1,3,4,5,6,7 for n>0,0,0,0,0,7,8
Empirical: rows n=1..7 are polynomials of degree 2*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
..0..0..0..0....0..1..0..0....0..0..1..1....0..0..0..1....1..1..0..0
..0..0..0..1....1..0..0..0....1..1..1..1....1..1..1..1....1..0..0..0
..1..1..1..0....0..0..1..1....1..1..1..1....1..1..1..1....0..0..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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