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A224409
T(n,k)=Number of nXk 0..1 arrays with rows unimodal and antidiagonals nondecreasing
12
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
OFFSET
1,1
COMMENTS
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
LINKS
FORMULA
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
EXAMPLE
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
CROSSREFS
Column 1 is A000079
Column 2 is A003946
Row 1 is A000124
Row 2 is A223764
Sequence in context: A296651 A297085 A224158 * A226870 A227751 A268995
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Apr 05 2013
STATUS
approved