A377063 Array read by antidiagonals: T(n,k) is the number of {-1,0,1} n X k matrices with all rows and columns summing to zero up to permutations of rows.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 4, 2, 1, 1, 1, 1, 10, 6, 3, 1, 1, 1, 1, 26, 30, 12, 3, 1, 1, 1, 1, 71, 166, 117, 18, 4, 1, 1, 1, 1, 197, 981, 1421, 345, 30, 4, 1, 1, 1, 1, 554, 5937, 20326, 9691, 1042, 42, 5, 1, 1, 1, 1, 1570, 36646, 307063, 336596, 63076, 2746, 63, 5, 1, 1

Offset: 0

Author

Andrew Howroyd, Oct 14 2024

Keywords

• nonn
• tabl

Comments

Columns are not permutable.

Equivalently, the number of n X k 0..2 arrays with row sums k and column sums n up to permutations of rows.

Examples

			Array begins:
===================================================
n\k | 0 1 2  3    4      5        6           7 ...
----+----------------------------------------------
  0 | 1 1 1  1    1      1        1           1 ...
  1 | 1 1 1  1    1      1        1           1 ...
  2 | 1 1 2  4   10     26       71         197 ...
  3 | 1 1 2  6   30    166      981        5937 ...
  4 | 1 1 3 12  117   1421    20326      307063 ...
  5 | 1 1 3 18  345   9691   336596    12650093 ...
  6 | 1 1 4 30 1042  63076  5328136   506525279 ...
  7 | 1 1 4 42 2746 369036 76292516 18490880339 ...
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..434 (first 29 antidiagonals)

Crossrefs

Main diagonal is A377064.

Rows n=0..4 are A000012, A000012, A257520, A377065, A377066.

Columns k=0..4 are A000012, A000012, A008619, A377067, A377068.

Cf. A334549.