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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.
2
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
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
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Apr 08 2020
STATUS
approved