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.

User: Abraham Maxfield

Abraham Maxfield's wiki page.

Abraham Maxfield has authored 4 sequences.

A373927 a(n) is the minimum number of hypercubes needed to admit a hole of size n in the 4D tesseractic honeycomb.

Original entry on oeis.org

16, 80, 106, 132
Offset: 0

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Author

Abraham Maxfield, Jun 22 2024

Keywords

Examples

			16 hypercubes surround a single vertex so a(0) = 16.
A 3 X 3 X 3 X 3 hypercube will admit a single hole in its center, so a(1) = 3*3*3*3 - 1 = 80.

Crossrefs

Cf. A345205 (3D equivalent), A235382 (2D equivalent).

A373612 Size of the largest polyiamond that can be enclosed in n cells on a triangular lattice.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 6, 6, 6, 7, 7, 10
Offset: 6

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Author

Abraham Maxfield, Jun 10 2024

Keywords

Examples

			A single triangular face takes 12 triangles to completely enclose so a(12) = 1.

Crossrefs

Cf. A290648. A257594 is the hexagonal tiling equivalent. A008642 is the square tiling equivalent (if prepended with 7 zeros).

A345206 Maximum number of unit cubes that can be fully enclosed in n unit cubes.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 14, 14, 16, 16, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 20, 20, 22, 22, 24, 24, 27
Offset: 8

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Author

Abraham Maxfield, Jun 11 2021

Keywords

Comments

Cubes are assumed to be aligned in a 3D grid. Cubes with an exposed edge or corner are not considered enclosed.
The Moore neighborhood of a cube in a 3-D grid consists of the 26 that share a face, an edge, or a vertex with it. - N. J. A. Sloane, Jul 12 2021

Examples

			a(26) = 1 as the number of neighbors in Moore's neighborhood is 26 in 3D.

Crossrefs

Cf. A345205. 3D equivalent to A008642.

A345205 Minimum number of unit cubes needed to fully enclose n unit cubes in 3D space.

Original entry on oeis.org

8, 26, 34, 42, 44, 52, 54, 56, 56, 64, 66, 68, 68, 76, 78, 80, 80, 82, 82, 90, 92, 94, 94, 96, 96, 98, 98, 98
Offset: 0

Views

Author

Abraham Maxfield, Jun 10 2021

Keywords

Comments

Cubes are assumed to be aligned in a 3D grid. Cubes with an exposed edge or corner are not considered enclosed.

Examples

			For a(1) the solution is the number of neighbors in Moore's neighborhood in 3 dimensions (3^3-1 = 26).
For a(2) the solution is the neighbors in Moore's neighborhood in 3 dimensions plus the number of neighbors in 2 dimensions (3^2-1 = 8).

Crossrefs

Cf. A345206, A235382 (2D equivalent), A007395 (1D equivalent), A024023.

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

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