A223770 T(n,k)=Number of nXk 0..1 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.

2, 4, 4, 7, 12, 7, 11, 28, 28, 11, 16, 56, 71, 56, 16, 22, 101, 155, 155, 101, 22, 29, 169, 317, 361, 317, 169, 29, 37, 267, 607, 782, 782, 607, 267, 37, 46, 403, 1097, 1601, 1748, 1601, 1097, 403, 46, 56, 586, 1887, 3141, 3699, 3699, 3141, 1887, 586, 56, 67, 826

Offset: 1

Author

R. H. Hardin Mar 27 2013

Keywords

• nonn
• tabl

Comments

Table starts

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

..4..12...28....56...101....169....267....403.....586.....826....1134.....1522

..7..28...71...155...317....607...1097...1887....3112....4950....7631....11447

.11..56..155...361...782...1601...3141...5907...10678...18618...31422....51505

.16.101..317...782..1748...3699...7564..14980...28778...53619...96979...170525

.22.169..607..1601..3699...8007..16742..34096...67890..132115..251110...465910

.29.267.1097..3141..7564..16742..35513..73427..149053..297518..583860..1125118

.37.403.1887..5907.14980..34096..73427.153450..314878..637213.1273700..2513629

.46.586.3112.10678.28778..67890.149053.314878..651075.1327905.2680691..5361746

.56.826.4950.18618.53619.132115.297518.637213.1327905.2723829.5530333.11141645

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..363

Crossrefs

Column 1 is A000124

Formula

Empirical: columns 1..7 are polynomials of degree 2*k for n>0,0,2,4,6,8,10