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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000292(n+1)

Column 2 is A001249

Row 1 is A223659

Sequence in context: A346460 A181717 A224173 * A223987 A224123 A273579

Adjacent sequences: A223861 A223862 A223863 * A223865 A223866 A223867

Keyword

nonn,tabl

Author

R. H. Hardin Mar 28 2013

Status

approved