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.

A108914 Number of regions formed inside square by diagonals and the segments joining the vertices to the points dividing the sides into n equal length segments.

Original entry on oeis.org

4, 32, 96, 188, 332, 460, 712, 916, 1204, 1488, 1904, 2108, 2716, 3080, 3532, 4068, 4772, 5140, 6016, 6392, 7188, 7992, 8936, 9260, 10484, 11312, 12208, 12968, 14396, 14660, 16504, 17220, 18436, 19680, 20756, 21548, 23692, 24728, 25992, 26868, 29204, 29704, 32176, 33068, 34444, 36552, 38552
Offset: 1

Views

Author

Len Smiley and Brian Wick ( mathclub(AT)math.uaa.alaska.edu ), Jul 19 2005

Keywords

Links

Crossrefs

A092098 is the corresponding count for triangles.
A355949 (vertices), A355948 (edges), A355992 (k-gons), A355838, A355798.

Formula

If n=1 or n is prime, a(n)=18*n^2-26*n+12.
If n is composite, vanishing regions from 3- and 4-fold concurrency must be subtracted.
a(n) = A355948(n) - A355949(n) + 1 by Euler's formula.

Extensions

a(23), a(33) corrected, a(41) and above by Scott R. Shannon, Jul 22 2022

A355949 Number of vertices formed in a square by straight line segments when connecting the four corner vertices to the points dividing the sides into n equal parts.

Original entry on oeis.org

5, 25, 81, 157, 301, 381, 665, 821, 1109, 1353, 1825, 1861, 2621, 2881, 3285, 3813, 4645, 4773, 5873, 5953, 6821, 7665, 8761, 8613, 10165, 10921, 11777, 12337, 14173, 13717, 16265, 16581, 17861, 19161, 20093, 20461, 23405, 24145, 25305, 25701, 28885, 28433, 31841, 32077, 33269, 35841, 38185
Offset: 1

Views

Author

Scott R. Shannon, Jul 21 2022

Keywords

Links

Crossrefs

Cf. A108914 (regions), A355948 (edges), A355992 (k-gons), A355839, A331452, A335678.

Formula

a(n) = A355948(n) - A108914(n) + 1 by Euler's formula.

A355948 Number of edges formed in a square by straight line segments when connecting the four corner vertices to the points dividing the sides into n equal parts.

Original entry on oeis.org

8, 56, 176, 344, 632, 840, 1376, 1736, 2312, 2840, 3728, 3968, 5336, 5960, 6816, 7880, 9416, 9912, 11888, 12344, 14008, 15656, 17696, 17872, 20648, 22232, 23984, 25304, 28568, 28376, 32768, 33800, 36296, 38840, 40848, 42008, 47096, 48872, 51296, 52568, 58088, 58136, 64016, 65144, 67712, 72392
Offset: 1

Views

Author

Scott R. Shannon, Jul 21 2022

Keywords

Comments

See A108914 for images of the squares.

Crossrefs

Cf. A108914 (regions), A355949 (vertices), A355992 (k-gons), A355840, A331452, A335678.

Formula

a(n) = A108914(n) + A355949(n) - 1 by 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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