A223987 T(n,k)=Number of nXk 0..3 arrays with rows unimodal and columns nondecreasing.

4, 16, 10, 50, 100, 20, 130, 684, 400, 35, 296, 3526, 5029, 1225, 56, 610, 14751, 44803, 25410, 3136, 84, 1163, 52591, 308470, 358118, 99634, 7056, 120, 2083, 165212, 1738756, 3770722, 2086196, 325120, 14400, 165, 3544, 468292, 8350154, 31585056

Offset: 1

Author

R. H. Hardin Mar 30 2013

Keywords

• nonn
• tabl

Comments

Table starts

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

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

..20...400.....5029......44803......308470.......1738756........8350154

..35..1225....25410.....358118.....3770722......31585056......219861244

..56..3136....99634....2086196....31831914.....378122264.....3661410444

..84..7056...325120....9647292...204647416....3322756326....43307637038

.120.14400...922768...37395816..1067023886...22985966340...392525216516

.165.27225..2346883..126087157..4710529013..131366850521..2873859236297

.220.48400..5462600..379654704.18159308422..642224541548.17659521902693

.286.81796.11818092.1040942916.62548820489.2756467192963.93729371629362

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..420

Crossrefs

Column 1 is A000292(n+1)

Column 2 is A001249

Row 1 is A223659

Row 2 is A223865

Formula

Empirical: columns k=1..7 are polynomials of degree 3*k

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