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
Andrew Howroyd, Table of n, a(n) for n = 0..500
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
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Oct 15 2024
STATUS
approved