A184129 T(n,k)=Number of nXk 0..3 arrays with rows and columns in nondecreasing order.

4, 10, 10, 20, 86, 20, 35, 561, 561, 35, 56, 2861, 14178, 2861, 56, 84, 12068, 276427, 276427, 12068, 84, 120, 43947, 4249486, 21907055, 4249486, 43947, 120, 165, 142376, 53817407, 1361812470, 1361812470, 53817407, 142376, 165, 220, 419213, 581588614

Offset: 1

Author

R. H. Hardin Jan 09 2011

Keywords

• nonn
• tabl

Comments

Empirical: T(n,k) for elements in 0..z is a polynomial in n of degree ((z+1)^k)-1 for fixed k

Table starts

...4......10...........20................35......................56

..10......86..........561..............2861...................12068

..20.....561........14178............276427.................4249486

..35....2861.......276427..........21907055..............1361812470

..56...12068......4249486........1361812470............348053502590

..84...43947.....53817407.......68564445616..........71759424776253

.120..142376....581588614.....2895890669208.......12323643023399737

.165..419213...5503143135...105444472863183.....1812407940171867666

.220.1139569..46473256070..3378291908588468...233154749874813919293

.286.2894178.355407459056.96731087997530019.26665385106037737856103

Examples

			Some solutions for 4X3
..0..0..2....0..0..3....0..2..2....0..0..3....0..0..3....0..0..2....0..0..2
..0..3..2....0..1..1....1..1..3....0..1..0....0..3..2....1..2..2....0..3..3
..1..0..3....1..3..1....3..0..1....0..1..3....3..0..3....2..2..1....2..1..2
..3..0..0....1..3..3....3..0..3....2..0..0....3..2..0....3..0..3....2..3..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..127

Crossrefs

Column 1 is A000292(n+1)

Diagonal is A162086