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A377065
Number of 3 X n 0..2 matrices with row sums n and column sums 3 up to permutations of rows.
4
1, 1, 2, 6, 30, 166, 981, 5937, 36646, 229350, 1451757, 9274057, 59699729, 386798777, 2520034050, 16497343046, 108454221206, 715629888822, 4737625385061, 31456633327905, 209418369288865, 1397521222483385, 9346484009527370, 62632803958053870, 420481623373564025
OFFSET
0,3
COMMENTS
Also, the number of 3 X n {-1,0,1} matrices with all rows and columns summing to zero up to permutations of rows.
LINKS
FORMULA
a(n) = (A172634(n) - 1)/6 + 1.
a(n) = (5 + Sum_{i=0..n} Sum_{j=0..i} (-1)^(n-i)*binomial(n, i)*binomial(i, j)^3)/6.
EXAMPLE
The a(2) = 2 matrices are:
[1 1] [2 0]
[1 1] [0 2]
[1 1] [1 1]
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) a(n)={(5+sum(i=0, n, sum(j=0, i, (-1)^(n-i)*binomial(n, i)*binomial(i, j)^3)))/6}
CROSSREFS
Row n=3 of A377063.
Sequence in context: A005432 A009422 A057221 * A180892 A366266 A196497
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Oct 15 2024
STATUS
approved