A346531 a(n) is the number of edges of the polycube called "tower" described in A221529 where n is the longest side of its base.

12, 12, 27, 36, 51, 72, 84, 105, 117, 144, 165

Offset: 1

Author

Omar E. Pol, Jul 22 2021

Keywords

• nonn
• more

Comments

The tower is a geometric object associated to all partitions of n.

The height of the tower equals A000041(n-1).

Examples

			For n = 1 the tower is a cube, and a cube has 12 edges, so a(1) = 12.
		

Crossrefs

Cf. A000203 (area of the terraces), A000041 (height of the terraces), A066186 (volume), A345023 (surface area), A346530 (number of faces), A346532 (number of vertices).

Cf. A325301 (analog for the pyramid described in A245092).

Cf. A221529, A236104, A237270, A237271, A237593, A336811, A338156, A340035, A340584.

Formula

a(n) = A346530(n) + A346532(n) - 2 (Euler's formula).