A224146 T(n,k) = Number of n X k 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

2, 4, 3, 7, 9, 4, 11, 22, 16, 5, 16, 46, 49, 25, 6, 22, 86, 124, 92, 36, 7, 29, 148, 275, 272, 155, 49, 8, 37, 239, 554, 691, 526, 242, 64, 9, 46, 367, 1037, 1573, 1509, 930, 357, 81, 10, 56, 541, 1831, 3296, 3827, 2985, 1536, 504, 100, 11, 67, 771, 3082, 6472, 8838

Offset: 1

Author

R. H. Hardin, Mar 31 2013

Keywords

• nonn
• tabl
• changed

Comments

Table starts

..2...4...7...11....16....22.....29......37......46......56.......67.......79

..3...9..22...46....86...148....239.....367.....541.....771.....1068.....1444

..4..16..49..124...275...554...1037....1831....3082....4984.....7789....11818

..5..25..92..272...691..1573...3296....6472...12058...21506....36961....61517

..6..36.155..526..1509..3827...8838...18969...38392...74053...137204...245636

..7..49.242..930..2985..8375..21183...49365..107697..222603...439909...837071

..8..64.357.1536..5471.16885..46586..117510..275557..608423..1277544..2571226

..9..81.504.2404..9431.31841..95455..259927..653980.1540542..3433254..7299542

.10.100.687.3602.15457.56783.184222..539980.1454873.3651978..8632537.19383022

.11.121.910.5206.24285.96579.337727.1062305.3058144.8167578.20458857.48492125

Examples

			Some solutions for n=3, k=4
..0..0..0..0....0..0..0..0....0..0..0..0....1..1..0..0....0..0..0..0
..1..1..0..0....0..1..0..0....0..1..1..0....1..1..0..0....0..0..0..1
..1..1..1..1....0..1..1..1....0..1..1..0....1..1..1..0....1..1..1..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..925

Crossrefs

Column 1 is A000027(n+1).

Column 2 is A000290(n+1).

Row 1 is A000124.

Row 2 is A223718.

Formula

Empirical: columns k=1..7 are polynomials of degree k for n>0,0,0,1,2,3,4.

Empirical: rows n=1..7 are polynomials of degree 2*n.