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

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

1,1

Comments

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

Links

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

Formula

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]

Example

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

Crossrefs

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

Sequence in context: A320948 A086885 A324598 * A331318 A376068 A082734

Adjacent sequences: A229791 A229792 A229793 * A229795 A229796 A229797

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 29 2013

Status

approved