A346530 -id:A346530 - cp's OEIS frontend

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

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).

A346532 a(n) is the number of vertices of the polycube called "tower" described in A221529 where n is the longest side of its base.

Original entry on oeis.org

8, 8, 18, 24, 33, 47, 55, 69, 77, 95, 108

Offset: 1

Omar E. Pol, Jul 22 2021

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

			For n = 1 the tower is a cube, and a cube has 8 vertices, so a(1) = 8.

Cf. A000203 (area of the terraces), A000041 (height of the terraces), A066186 (volume), A345023 (surface area), A346530 (number of faces), A346531 (number of edges).
Cf. A325302 (analog for the pyramid described in A245092).
Cf. A221529, A236104, A237270, A237271, A237593, A336811, A338156, A340035, A340584.

a(n) = A346531(n) - A346530(n) + 2 (Euler's formula).

cp's OEIS Frontend

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.

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