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A377067
Number of n X 3 0..2 matrices with row sums 3 and column sums n up to permutations of rows.
4
1, 1, 4, 6, 12, 18, 30, 42, 63, 85, 118, 154, 204, 258, 330, 408, 507, 615, 748, 892, 1066, 1254, 1476, 1716, 1995, 2295, 2640, 3010, 3430, 3880, 4386, 4926, 5529, 6171, 6882, 7638, 8470, 9352, 10318, 11340, 12453, 13629, 14904, 16248, 17700, 19228, 20872, 22600, 24453, 26397, 28476
OFFSET
0,3
COMMENTS
Also, the number of n X 3 {-1,0,1} matrices with all rows and columns summing to zero up to permutations of rows.
FORMULA
G.f.: (2/(1 - x^3) - 1)/((1 - x)*(1 - x^2)^3).
G.f.: (1 - x + x^2)/((1 - x)^5*(1 + x)^2*(1 + x + x^2)).
EXAMPLE
The a(2) = 4 matrices are:
[1 1 1] [2 1 0] [2 0 1] [1 2 0]
[1 1 1] [0 1 2] [0 2 0] [1 0 2]
The a(3) = 6 matrices are:
[1 1 1] [2 1 0] [2 0 1] [1 2 0] [2 1 0] [2 0 1]
[1 1 1] [0 1 2] [0 2 0] [1 0 2] [1 0 2] [1 2 0]
[1 1 1] [1 1 1] [1 1 1] [1 1 1] [0 2 1] [0 1 2]
PROG
(PARI) Vec((1 - x + x^2)/((1 - x)^5*(1 + x)^2*(1 + x + x^2)) + O(x^51))
CROSSREFS
Column k=3 of A377063.
Sequence in context: A217259 A014574 A258838 * A034425 A073123 A079865
KEYWORD
nonn,easy
AUTHOR
Andrew Howroyd, Oct 15 2024
STATUS
approved