A202784 T(n,k) is the number of n X n 0..k arrays with row and column sums equal.

1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 9, 14, 1, 1, 5, 16, 87, 140, 1, 1, 6, 25, 340, 5673, 4322, 1, 1, 7, 36, 1001, 89520, 2577513, 434542, 1, 1, 8, 49, 2442, 790425, 290838284, 8459809773, 144109562, 1, 1, 9, 64, 5215, 4756140, 11991502235, 12092687195284, 207495141083975, 165431317452, 1

Offset: 0

Author

R. H. Hardin, Dec 24 2011

Keywords

• nonn
• tabl

Examples

			Table starts
n\k | 0            1               2              3                4
----+-------------------------------------------------------------------
  0 | 1            1               1              1                1 ...
  1 | 1            2               3              4                5 ...
  2 | 1            4               9             16               25 ...
  3 | 1           14              87            340             1001 ...
  4 | 1          140            5673          89520           790425 ...
  5 | 1         4322         2577513      290838284      11991502235 ...
  6 | 1       434542      8459809773 12092687195284 3632894572698505 ...
  7 | 1    144109562 207495141083975 ...
  8 | 1 165431317452 ...
  ...
Some solutions for n=4 k=3
..3..1..2..1....2..2..0..3....1..1..1..2....1..3..0..0....1..2..0..2
..2..3..2..0....1..2..2..2....3..0..1..1....1..0..1..2....3..1..0..1
..2..2..0..3....3..0..3..1....0..3..2..0....2..0..1..1....0..0..3..2
..0..1..3..3....1..3..2..1....1..1..1..2....0..1..2..1....1..2..2..0
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..119 (first 15 antidiagonals; terms up to n=61 from R. H. Hardin)

Crossrefs

Rows n=0..5 are A000012, A000027(k+1), A000290(k+1), A202785, A202786, A202787.

Columns k=1..15 are A067209, A067210, A067211, A067212, A067213, A067214, A067215, A067216, A067217, A067218, A067219, A067220, A067221, A067222, A067223.

Cf. A008300, A257493.

Extensions

Added crossrefs. - R. H. Hardin, Jan 05 2012

Row and column zero inserted by Andrew Howroyd, Oct 14 2024