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.

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A331456 Number of regions in an equal-armed cross with arms of length n (see Comments for definition).

Original entry on oeis.org

4, 104, 568, 1900, 4808, 10180, 19180, 33132, 53628, 82432, 121448, 172948, 239356, 323168, 427272, 554892, 709476, 893772, 1111588, 1367292, 1664604, 2008240, 2402560, 2852532, 3363280, 3938712, 4585568, 5308720, 6112736, 7006068, 7994412, 9084788, 10281812
Offset: 0

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Comments

This cross of height n consists of a central square with 4 arms of length n.
There are 4n+1 squares in all. The number of vertices is 8n+4.
Now join every pair of vertices by a line segment, provided the line does not extend beyond the boundary of the cross. The sequence gives the number of regions in the resulting figure.
See A337641 for information about these regions, their numbers of sides, their coordinates, and for further illustrations. - N. J. A. Sloane, Sep 17 2020

Crossrefs

Cf. A333035 (vertices), A333036 (edges), A333037 (n-gons), A337641.
See A331455 for a different family of crosses.
A331452 is a similar sequence for a rectangular region; A007678 for a polygonal region.
Cf. A331458.

Extensions

a(11) and beyond from Lars Blomberg, May 30 2020
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