A346532 -id:A346532 - cp's OEIS frontend

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

Omar E. Pol, Jul 22 2021

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

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

			For n = 1 the tower is a cube, and a cube has 6 faces, so a(1) = 6.

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.

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

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.

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Jul 22 2021

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

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

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

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.

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

cp's OEIS Frontend

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.

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