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.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,1,-3,-1,1,3,-1,-2,1).
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
KEYWORD
nonn,easy
AUTHOR
Andrew Howroyd, Oct 15 2024
STATUS
approved