A346530 a(n) is the number of faces of the polycube called "tower" described in A221529 where n is the longest side of its base.

6, 6, 11, 14, 20, 27, 31, 38, 42, 51, 59

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 6 faces, so a(1) = 6.
		

Crossrefs

Cf. A000203 (area of the terraces), A000041 (height of the terraces), A066186 (volume), A345023 (surface area), A346531 (number of edges), A346532 (number of vertices).

Cf. A325300 (analog for the pyramid described in A245092).

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

Formula

a(n) = A346531(n) - A346532(n) + 2 (Euler's formula).