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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A274822 Total number of regions in all arrangements of n circles in the affine plane, including the regions that do not belong to the circles.

Original entry on oeis.org

1, 7, 66
Offset: 1

Views

Author

Omar E. Pol, Jul 07 2016

Keywords

Comments

Consider the arrangements of n circles described in A250001.

Crossrefs

Row sums of triangle A274818.
For another version see A274823.
Cf. A250001, A274776.

A274823 Total number of regions in all arrangements of n circles in the affine plane, excluding the regions that do not belong to the circles.

Original entry on oeis.org

1, 7, 65
Offset: 1

Views

Author

Omar E. Pol, Jul 07 2016

Keywords

Comments

In other words: not counting the regions between circles.
Consider the arrangements of n circles described in A250001.

Crossrefs

Row sums of triangle A274819.
For another version see A274822.
Cf. A250001, A274777.

A285996 Triangle read by rows, 1<=k<=n, T(n,k) = number of arrangements of n circles in the affine plane having k separated islands.

Original entry on oeis.org

1, 2, 1, 11, 2, 1, 156, 14, 2, 1
Offset: 1

Views

Author

Omar E. Pol, May 21 2017

Keywords

Comments

Consider the rules for the arrangements of n circles described in A250001.
Note that T(4,1) = 156 includes the arrangement of 4 circles in which there is a little circle that is surrounded by the union of three solid circles, because the little circle is an inland island, or lake island, which does not count. So there is only one separated island. Hence T(4,2) = 14 does not include the mentioned arrangement.
Question: is 1 together with the first column of the triangle the same as A275923?

Examples

			Triangle begins:
1;
2,   1;
11,  2,  1;
156, 14, 2, 1;

Crossrefs

Another version of A252158.
Row sums give A250001, n >= 1.
Right border gives A000012.
Cf. A249752, A275923.

A274702 a(n) = number of arrangements of n circles in the affine plane in which all circles share part of their boundary with the boundary of the union of all the circles.

Original entry on oeis.org

1, 2, 6, 47
Offset: 1

Views

Author

Omar E. Pol, Jul 06 2016

Keywords

Comments

Consider the arrangements of n circles described in A250001.

Crossrefs

Leading diagonal of triangle A249752.
Cf. A250001.

A287149 Number of arrangements of n circles in the affine plane having only one island or region, which is formed by the union of all solid circles of the arrangement.

Original entry on oeis.org

1, 1, 2, 11, 155
Offset: 0

Views

Author

Omar E. Pol, May 21 2017

Keywords

Comments

A subset of the arrangements of n circles described in A250001.
Note that a(4) = 155 does not include the arrangement of four circles in which there is a little circle that is surrounded by the union of three solid circles, because in that arrangement there are two islands or regions, not one.

Crossrefs

1 together with the first column of A252158.
First differs from A275923 at a(4).
Cf. A250001.

A317967 Number of connected line structures or "topoglyphs" with n regions.

Original entry on oeis.org

1, 1, 4, 23, 186
Offset: 0

Views

Author

N. J. A. Sloane, Aug 27 2018

Keywords

Comments

The precise definition is hard to understand from the article. But Marcel Golay was a famous scientist, and this article seems to have been overlooked, so the sequences are worth placing on record.

References

  • Marcel J. E. Golay, Topoglyphs, IEEE Trans. Computers, C-27 (No. 2, Feb. 1978), 164-167.

Links

Crossrefs

Cf. A317968.
A250001 is a similar sequence.

A339266 Numbers of connected arrangements of n equal circles in the affine plane, in the sense that the union of the boundaries of the circles is a connected set.

Original entry on oeis.org

1, 1, 1, 4, 29
Offset: 0

Views

Author

Ya-Ping Lu, Nov 29 2020

Keywords

Examples

			Configurations for a(1) through a(4) are given in the links.

Links

Crossrefs

Cf. A250001, A275923, A275924, A288554-A288568, A296407

A285995 Number of arrangements of n circles in the affine plane such that at least two of the circles meet.

Original entry on oeis.org

0, 0, 1, 10, 164
Offset: 0

Views

Author

Omar E. Pol, May 17 2017

Keywords

Comments

A subset the arrangements of n circles described in A250001, which is the main entry for this sequence.
See also the comments related to A000081 from Benoit Jubin and N. J. A. Sloane in A250001.

Crossrefs

Row sums of A261070 except its column k = 0.
Cf. A000081, A250001.

Formula

a(n) = A250001(n) - A000081(n+1).

A288563 Number of one-sided arrangements of n pseudo-circles in the affine plane.

Original entry on oeis.org

1, 1, 3, 14, 200, 30630
Offset: 0

Views

Author

N. J. A. Sloane, Jun 13 2017, based on information supplied by Jon Wild on Aug 31 2016

Keywords

Comments

These counts have not been reduced for mirror symmetry.
See A250001, the main entry for this problem, for further information.

Crossrefs

Cf. A250001, A275923, A275924, A288554-A288568.

A317968 Number of (not necessarily connected) line structures or "topoglyphs" with n regions.

Original entry on oeis.org

1, 1, 5, 28, 220
Offset: 0

Views

Author

N. J. A. Sloane, Aug 27 2018

Keywords

Comments

The precise definition is hard to understand from the article. But Marcel Golay was a famous scientist, and this article seems to have been overlooked, so the sequences are worth placing on record.

References

  • Marcel J. E. Golay, Topoglyphs, IEEE Trans. Computers, C-27 (No. 2, Feb. 1978), 164-167.

Links

Crossrefs

Cf. A317967.
A250001 is a similar sequence.
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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