A224158 T(n,k)=Number of nXk 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing

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

Offset

1,1

Comments

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

Links

R. H. Hardin, Table of n, a(n) for n = 1..797

Formula

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

Example

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

Crossrefs

Column 1 is A000079

Column 2 is A003946

Row 1 is A000124

Row 2 is A223764

Sequence in context: A227558 A296651 A297085 * A224409 A226870 A227751

Adjacent sequences: A224155 A224156 A224157 * A224159 A224160 A224161

Keyword

nonn,tabl

Author

R. H. Hardin Mar 31 2013

Status

approved