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

1,3

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)

Links

Table of n, a(n) for n=1..12.

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

Adjacent sequences: A195795 A195796 A195797 * A195799 A195800 A195801

Keyword

nonn,hard,more

Author

R. H. Hardin, Sep 23 2011

Status

approved