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

0,3

Links

Table of n, a(n) for n=0..40.

Example

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.

Sequence in context: A192303 A301785 A066280 * A192243 A292104 A136113

Adjacent sequences: A333883 A333884 A333885 * A333887 A333888 A333889

Keyword

nonn

Author

Andrew Howroyd, Apr 08 2020

Status

approved