A224409 T(n,k)=Number of nXk 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

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

R. H. Hardin, Table of n, a(n) for n = 1..2445

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

Adjacent sequences: A224406 A224407 A224408 * A224410 A224411 A224412

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 05 2013

Status

approved