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, 2, 8, 16, 64, 1184, 5300, 130324, 14748808, 421963232, 54990266540

Offset: 1

Author

R. H. Hardin, Sep 23 2011

Keywords

• nonn
• hard
• more

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)

Examples

			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.