A223864 T(n,k)=Number of nXk 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

4, 16, 10, 50, 100, 20, 130, 684, 400, 35, 296, 3526, 4884, 1225, 56, 610, 14751, 41682, 24199, 3136, 84, 1163, 52591, 273959, 315124, 93731, 7056, 120, 2083, 165212, 1477240, 3017129, 1771012, 303560, 14400, 165, 3544, 468292, 6818350, 22852913

Offset: 1

Author

R. H. Hardin Mar 28 2013

Keywords

• nonn
• tabl

Comments

Table starts

...4....16.......50.......130.........296...........610...........1163

..10...100......684......3526.......14751.........52591.........165212

..20...400.....4884.....41682......273959.......1477240........6818350

..35..1225....24199....315124.....3017129......22852913......144081276

..56..3136....93731...1771012....23738426.....243933798.....2030417942

..84..7056...303560...8008548...145947740....1989679315....21476594002

.120.14400...857696..30627033...740441932...13140481520...181330154458

.165.27225..2175884.102479569..3217594840...73068868012..1271807435844

.220.48400..5058530.307435001.12305144319..352040804450..7630189031428

.286.81796.10940664.842078930.42270004211.1502130487437.40055722078772

Examples

			Some solutions for n=3 k=4
..0..0..0..0....0..2..1..1....0..1..3..2....0..2..2..0....0..1..1..3
..0..0..0..1....0..2..3..1....0..2..3..2....1..3..3..2....0..1..3..3
..2..3..2..2....0..2..3..3....1..3..3..3....3..3..3..2....1..3..3..3
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..312

Crossrefs

Column 1 is A000292(n+1)

Column 2 is A001249

Row 1 is A223659

Formula

Empirical: columns k=1..7 are polynomials of degree 3*k for n>0,0,0,1,2,4,6

Empirical: rows n=1..7 are polynomials of degree 6*n