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A229417
T(n,k) = number of n X n 0..k zero-diagonal arrays with corresponding row and column sums equal.
6
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Sep 22 2013
STATUS
approved