A333886 Number of non-isomorphic 4 X 4 nonnegative integer symmetric matrices with all row and column sums equal to n up to permutations of rows and columns.

1, 1, 5, 12, 33, 74, 163, 319, 596, 1044, 1754, 2820, 4394, 6629, 9756, 14018, 19743, 27286, 37111, 49707, 65699, 85756, 110691, 141382, 178882, 224309, 278990, 344342, 422000, 513718, 621506, 747493, 894105, 1063920, 1259823, 1484886, 1742533, 2036377, 2370431, 2748936, 3176544

Offset: 0

Author

Andrew Howroyd, Apr 08 2020

Keywords

• nonn

Examples

			The a(2) = 5 matrices are:
  [0 0 0 2]  [0 0 0 2]  [0 0 1 1]  [0 0 1 1]  [0 0 1 1]
  [0 0 2 0]  [0 1 1 0]  [0 0 1 1]  [0 1 0 1]  [0 2 0 0]
  [0 2 0 0]  [0 1 1 0]  [1 1 0 0]  [1 0 1 0]  [1 0 0 1]
  [2 0 0 0]  [2 0 0 0]  [1 1 0 0]  [1 1 0 0]  [1 0 1 0]
.
The a(3) = 12 matrices are:
  [0 0 0 3] [0 0 1 2] [0 0 1 2] [0 0 1 2] [0 0 1 2] [0 1 1 1]
  [0 0 3 0] [0 0 2 1] [0 1 1 1] [0 1 2 0] [0 2 1 0] [1 0 1 1]
  [0 3 0 0] [1 2 0 0] [1 1 1 0] [1 2 0 0] [1 1 0 1] [1 1 0 1]
  [3 0 0 0] [2 1 0 0] [2 1 0 0] [2 0 0 1] [2 0 1 0] [1 1 1 0]
.
  [0 0 0 3] [0 0 1 2] [0 0 1 2] [0 0 1 2] [0 1 1 1] [1 0 1 1]
  [0 1 2 0] [0 2 1 0] [0 3 0 0] [0 3 0 0] [1 1 0 1] [0 3 0 0]
  [0 2 1 0] [1 1 1 0] [1 0 1 1] [1 0 2 0] [1 0 2 0] [1 0 1 1]
  [3 0 0 0] [2 0 0 1] [2 0 1 0] [2 0 0 1] [1 1 0 1] [1 0 1 1]
		

Crossrefs

Row n=4 of A333737.