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

1,1

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

Links

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

Example

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

Crossrefs

Column 1 is A000292(n+1)

Diagonal is A162086

Sequence in context: A310336 A227060 A278727 * A202581 A201729 A310337

Adjacent sequences: A184126 A184127 A184128 * A184130 A184131 A184132

Keyword

nonn,tabl

Author

R. H. Hardin Jan 09 2011

Status

approved