login
A195798
Number of triangular n X n X n 0..1 arrays with all rows and diagonals having the same length having the same sum, with corners zero.
1
1, 1, 2, 8, 16, 64, 1184, 5300, 130324, 14748808, 421963232, 54990266540
OFFSET
1,3
COMMENTS
From Pontus von Brömssen, Sep 08 2022: (Start)
For n <= 6, all solutions are rotationally symmetric, which implies that a(n) = 2^(A007997(n+4)-1). But for n >= 7 there exist asymmetric solutions like
0
0 0
0 0 1
0 1 0 0
1 0 0 0 0
0 0 0 0 1 0
0 0 0 1 0 0 0.
(End)
EXAMPLE
Some solutions for n=5
......0..........0..........0..........0..........0..........0..........0
.....0.0........0.0........0.0........0.1........0.1........0.1........0.1
....0.1.0......1.0.1......1.1.1......0.0.0......0.1.0......1.0.1......1.1.1
...0.1.1.0....0.0.0.0....0.1.1.0....1.0.0.0....1.1.1.0....1.0.0.0....1.1.1.0
..0.0.0.0.0..0.0.1.0.0..0.0.1.0.0..0.0.0.1.0..0.0.0.1.0..0.0.1.1.0..0.0.1.1.0
CROSSREFS
Column 1 of A195805.
Cf. A007997.
Sequence in context: A094014 A098232 A354275 * A100736 A099888 A249308
KEYWORD
nonn,hard,more
AUTHOR
R. H. Hardin, Sep 23 2011
STATUS
approved