A162086 -id:A162086 - cp's OEIS frontend

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

R. H. Hardin Jan 09 2011

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

			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

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

Column 1 is A000292(n+1)

Diagonal is A162086

A229794 T(n,k)=Number of n X n 0..k arrays with rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

2, 3, 7, 4, 29, 45, 5, 86, 1169, 650, 6, 205, 14178, 250841, 24520, 7, 421, 102251, 21907055, 318174607, 2625117, 8, 777, 520017, 733861607, 348053502590, 2533164987353, 836488618, 9, 1324, 2066505, 13111482259, 83399309397669

Offset: 1

R. H. Hardin, Sep 29 2013

Table starts
.....2.........3............4..............5................6
.....7........29...........86............205..............421
....45......1169........14178.........102251...........520017
...650....250841.....21907055......733861607......13111482259
.24520.318174607.348053502590.83399309397669.7470491620551006

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

R. H. Hardin, Table of n, a(n) for n = 1..63

Column 1 is A089006
Column 2 is A162085
Column 3 is A162086
Column 4 is A162087
Column 5 is A162088
Column 6 is A162089
Column 7 is A162090

Empirical for row n:
n=1: a(n) = 1*n + 1
n=2: a(n) = (1/3)*n^4 + (7/6)*n^3 + (13/6)*n^2 + (7/3)*n + 1
n=3: [polynomial of degree 9]
n=4: [polynomial of degree 16]

cp's OEIS Frontend

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

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