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

Author

R. H. Hardin Mar 31 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000079

Column 2 is A003946

Row 1 is A000124

Row 2 is A223764

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