A333886 - OEIS

%I #8 Apr 09 2020 03:13:55

%S 1,1,5,12,33,74,163,319,596,1044,1754,2820,4394,6629,9756,14018,19743,

%T 27286,37111,49707,65699,85756,110691,141382,178882,224309,278990,

%U 344342,422000,513718,621506,747493,894105,1063920,1259823,1484886,1742533,2036377,2370431,2748936,3176544

%N 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.

%e The a(2) = 5 matrices are:

%e   [0 0 0 2]  [0 0 0 2]  [0 0 1 1]  [0 0 1 1]  [0 0 1 1]

%e   [0 0 2 0]  [0 1 1 0]  [0 0 1 1]  [0 1 0 1]  [0 2 0 0]

%e   [0 2 0 0]  [0 1 1 0]  [1 1 0 0]  [1 0 1 0]  [1 0 0 1]

%e   [2 0 0 0]  [2 0 0 0]  [1 1 0 0]  [1 1 0 0]  [1 0 1 0]

%e .

%e The a(3) = 12 matrices are:

%e   [0 0 0 3] [0 0 1 2] [0 0 1 2] [0 0 1 2] [0 0 1 2] [0 1 1 1]

%e   [0 0 3 0] [0 0 2 1] [0 1 1 1] [0 1 2 0] [0 2 1 0] [1 0 1 1]

%e   [0 3 0 0] [1 2 0 0] [1 1 1 0] [1 2 0 0] [1 1 0 1] [1 1 0 1]

%e   [3 0 0 0] [2 1 0 0] [2 1 0 0] [2 0 0 1] [2 0 1 0] [1 1 1 0]

%e .

%e   [0 0 0 3] [0 0 1 2] [0 0 1 2] [0 0 1 2] [0 1 1 1] [1 0 1 1]

%e   [0 1 2 0] [0 2 1 0] [0 3 0 0] [0 3 0 0] [1 1 0 1] [0 3 0 0]

%e   [0 2 1 0] [1 1 1 0] [1 0 1 1] [1 0 2 0] [1 0 2 0] [1 0 1 1]

%e   [3 0 0 0] [2 0 0 1] [2 0 1 0] [2 0 0 1] [1 1 0 1] [1 0 1 1]

%Y Row n=4 of A333737.

%K nonn

%O 0,3

%A _Andrew Howroyd_, Apr 08 2020