A377068 - OEIS

%I #7 Oct 15 2024 15:46:50

%S 1,1,10,30,117,345,1042,2746,7063,16759,38440,83476,175473,354105,

%T 694278,1318222,2440888,4402852,7770908,13418156,22734824,37807500,

%U 61839510,99526422,157858478,246864782,381087734,580990046,875572808,1304930876,1924761300,2810843268

%N Number of n X 4 0..2 matrices with row sums 4 and column sums n up to permutations of rows.

%C Also, the number of n X 4 {-1,0,1} matrices with all rows and columns summing to zero up to permutations of rows.

%e The a(2) = 10 matrices are:

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

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

%e .

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

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

%Y Column k=4 of A377063.

%Y Cf. A172642, A377066, A377067.

%K nonn

%O 0,3

%A _Andrew Howroyd_, Oct 15 2024