A300693 a(n) = number of edges in a concertina n-cube.

0, 1, 6, 42, 344, 3230, 34452

Offset: 0

Author

Tilman Piesk, Apr 03 2018

Keywords

• nonn
• more

Comments

n-place formulas in first-order logic like Ax Ey P(x, y) can be ordered by implication. This Hasse diagram has A000629(n) vertices and a(n) edges.

This is the second diagonal on the right in A300700, the triangle of faces in the concertina n-cube.

The corresponding sequence for cocoon concertina n-cubes, which have more internal vertices and edges, is A300694.

Links

• Tilman Piesk, Formulas in predicate logic (Wikiversity)
• Tilman Piesk, Image of a concertina square with 6 and cube with 42 edges
• Tilman Piesk, Lists of edges for n=2..5
• Tilman Piesk, Python code used to generate the sequence

Crossrefs

Cf. A300700, A000629, A300694.

Formula

a(n) = A300700(n, n-1).