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

1,1

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

Links

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

Formula

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

Example

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

Crossrefs

Column 1 is A000124

Sequence in context: A283543 A297682 A297607 * A223777 A227089 A225900

Adjacent sequences: A223767 A223768 A223769 * A223771 A223772 A223773

Keyword

nonn,tabl

Author

R. H. Hardin Mar 27 2013

Status

approved