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

1,1

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

Links

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

Formula

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

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

Example

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

Crossrefs

Column 1 is A000292(n+1)

Column 2 is A001249

Row 1 is A223659

Row 2 is A223865

Sequence in context: A181717 A224173 A223864 * A224123 A273579 A147560

Adjacent sequences: A223984 A223985 A223986 * A223988 A223989 A223990

Keyword

nonn,tabl

Author

R. H. Hardin Mar 30 2013

Status

approved