A229417 T(n,k) = number of n X n 0..k zero-diagonal arrays with corresponding row and column sums equal.

1, 1, 2, 1, 3, 10, 1, 4, 45, 152, 1, 5, 136, 4743, 7736, 1, 6, 325, 59008, 3801411, 1375952, 1, 7, 666, 426425, 345706336, 23938685973, 877901648, 1, 8, 1225, 2164680, 11782824375, 28256240134144, 1215663478473627, 2046320373120, 1, 9, 2080

Offset

1,3

Comments

Table starts

.........1................1....................1................1............1

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

........10...............45..................136..............325..........666

.......152.............4743................59008...........426425......2164680

......7736..........3801411............345706336......11782824375.213067487016

...1375952......23938685973.......28256240134144.7093199984236625

.877901648.1215663478473627.33097994593655140864

Links

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

Formula

Empirical for row n:

n=1: a(n) = 1

n=2: a(n) = n + 1

n=3: a(n) = (1/2)*n^4 + 2*n^3 + (7/2)*n^2 + 3*n + 1

n=4: [polynomial of degree 9]

Row n is an Ehrhart polynomial of degree (n-1)^2 for the polytope of x(i,j), i,j = 1..n for j <> i, with 0 <= x(i,j) <= 1 and Sum_i x(i,j) = Sum_i x(j,i). - Robert Israel, Mar 30 2023

T(n,k) = A229870(n,k) / (k + 1)^n. - Andrew Howroyd, Mar 30 2023

Example

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

Crossrefs

Columns 1..3 are A007080, A229415, A229416.

Rows 3..6 are A037270(n+1), A229418, A229419, A229420.

Cf. A229870.

Sequence in context: A301282 A246063 A332064 * A337890 A337888 A337887

Adjacent sequences: A229414 A229415 A229416 * A229418 A229419 A229420

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 22 2013

Status

approved