cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A325300 a(n) is the number of faces of the stepped pyramid with n levels described in A245092.

Original entry on oeis.org

6, 9, 15, 20, 24, 31, 35, 42, 49, 59, 63, 72, 76, 84, 95, 106, 110, 121, 125
Offset: 1

Views

Author

Omar E. Pol, Apr 16 2019

Keywords

Comments

To calculate a(n) consider that levels greater than n do not exist.
The shape of the n-th level of the pyramid allows us to know if n is prime (see the Formula section).
For more information about the sequences that we can see in the pyramid see A262626.

Examples

			For n = 1 the first level of the stepped pyramid (starting from the top) is a cube, and a cube has six faces, so a(1) = 6.

Links

Crossrefs

Cf. A325301 (number of edges), A325302 (number of vertices).
Cf. A196020, A215848, A235791, A236104, A237270, A237271, A237591, A237593, A245092, A262626, A299692, A323645, A323648.

Formula

a(n) = A325301(n) - A325302(n) + 2 (Euler's formula).
a(n) = A323645(n) + 3.
a(n) = a(n-1) + 4 iff n is a prime > 3 (A215848).

A325302 a(n) is the number of vertices of the stepped pyramid with n levels described in A245092.

Original entry on oeis.org

8, 14, 23, 33, 41, 55, 63, 77, 91, 108, 116, 134, 142, 158, 180, 202, 210, 232, 240
Offset: 1

Views

Author

Omar E. Pol, Apr 16 2019

Keywords

Comments

To calculate a(n) consider that levels greater than n do not exist.

Examples

			For n = 1 the first level of the stepped pyramid (starting from the top) is a cube, and a cube has 8 vertices, so a(1) = 8.

Links

Crossrefs

Cf. A325300 (number of faces), A325301 (number of edges).
Cf. A196020, A235791, A236104, A237270, A237271, A237591, A237593, A245092, A262626, A294723, A323648.

Formula

a(n) = A325301(n) - A325300(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

Views

Author

Omar E. Pol, Jul 22 2021

Keywords

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).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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