A229870 T(n,k)=Number of n X n 0..k arrays with corresponding row and column sums equal

2, 3, 8, 4, 27, 80, 5, 64, 1215, 2432, 6, 125, 8704, 384183, 247552, 7, 216, 40625, 15106048, 923742873, 88060928, 8, 343, 143856, 266515625, 354003288064, 17451302074317, 112371410944, 9, 512, 420175, 2805425280, 36821326171875

Offset

1,1

Comments

Table starts

......2.........3............4..............5................6...........7

......8........27...........64............125..............216.........343

.....80......1215.........8704..........40625...........143856......420175

...2432....384183.....15106048......266515625.......2805425280.20610104767

.247552.923742873.354003288064.36821326171875.1656812779036416

Links

R. H. Hardin, Table of n, a(n) for n = 1..43

Formula

Empirical for row n:

n=1: a(n) = n + 1

n=2: a(n) = n^3 + 3*n^2 + 3*n + 1

n=3: [polynomial of degree 7]

n=4: [polynomial of degree 13]

Example

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

Crossrefs

Row 2 is A000578(n+1)

Row 3 is A168364(n+1)

Sequence in context: A093898 A194931 A195248 * A202651 A334859 A084110

Adjacent sequences: A229867 A229868 A229869 * A229871 A229872 A229873

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 01 2013

Status

approved