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

Author

R. H. Hardin, Oct 01 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Row 2 is A000578(n+1)

Row 3 is A168364(n+1)

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]