A224173 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, 4739, 1225, 56, 610, 14751, 38561, 22988, 3136, 84, 1163, 52591, 242114, 272130, 87878, 7056, 120, 2083, 165212, 1253770, 2335459, 1460836, 282372, 14400, 165, 3544, 468292, 5588411, 15925611

Offset

1,1

Comments

Table starts

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

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

..20...400.....4739.....38561......242114......1253770........5588411

..35..1225....22988....272130.....2335459.....15925611.......91494280

..56..3136....87878...1460836....16625026....143558572.....1012166273

..84..7056...282372...6425876....95808564...1038484760.....8857798353

.120.14400...794220..24197608...468021427...6360047093....65713691148

.165.27225..2010035..80350989..1994287334..33901838632...426013124302

.220.48400..4668304.240416852..7568051210.160168789130..2451904991177

.286.81796.10095924.658890738.25994968917.680269560125.12667946702827

Links

R. H. Hardin, Table of n, a(n) for n = 1..178

Formula

Empirical: columns k=1..7 are polynomials of degree 3*k for n>0,0,0,3,6,9,12

Empirical: rows n=1..5 are polynomials of degree 6*n for k>0,0,0,2,6

Example

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

Crossrefs

Column 1 is A000292(n+1)

Column 2 is A001249

Row 1 is A223659

Row 2 is A223865

Sequence in context: A067178 A346460 A181717 * A223864 A223987 A224123

Adjacent sequences: A224170 A224171 A224172 * A224174 A224175 A224176

Keyword

nonn,tabl

Author

R. H. Hardin Mar 31 2013

Status

approved