A250001 -id:A250001 - cp's OEIS frontend

A383744 The number of distinct straightedge-and-compass constructions that can be made with a total of n lines and circles up to rigid motion.

1, 2, 2, 6, 44, 1000, 90585

Offset: 0

Peter Kagey and N. J. A. Sloane, May 08 2025

A straightedge-and-compass construction starts with 2 points marked on the plane, traditionally (0,0) and (1,0). One can use a straightedge to draw a line between two marked points or a compass to draw a circle centered at a marked point through another marked point. New points occur at the intersections of lines or circles with lines or circles.

In this sequence, two constructions are considered the same if you can rotate, reflect, or translate one to get the other.

			For example the following two constructions are considered the same:
(1) Draw a circle centered at (0,0) through (1,0), and then draw a line through (0,0) and (1,0).
(2) Draw a line through (0,0) and (0,1) and then draw a circle centered at (1,0) through (0,0).

Cf. A241600, A250001, A383082, A383083, A383273

A288555 Number of one-sided arrangements of n circles in the affine plane.

Original entry on oeis.org

1, 1, 3, 14, 200

Offset: 0

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

These counts are not reduced for mirror symmetry.

See A250001, the main entry for this problem, for further information.

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

A288556 Number of connected one-sided arrangements of n circles in the affine plane, in the sense that the union of the solid circles is a connected set.

Original entry on oeis.org

1, 1, 2, 11, 183

Offset: 0

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

These counts are not reduced for mirror symmetry.

See A250001, the main entry for this problem, for further information.

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

A288557 Number of connected one-sided arrangements of n 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, 6, 139

Offset: 0

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

These counts are not reduced for mirror symmetry.

See A250001, the main entry for this problem, for further information.

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

A288560 Number of connected arrangements of n pseudo-circles in the affine plane, in the sense that the union of the solid pseudo-circles is a connected set.

Original entry on oeis.org

1, 1, 2, 11, 156, 16782

Offset: 0

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

Arrangements in A288559 that are connected (in the sense that the union of the solid pseudo-circles is a connected set).
These counts have been reduced for mirror symmetry.
See A250001, the main entry for this problem, for further information.

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

A288561 Number of connected arrangements of n pseudo-circles in the affine plane, in the sense that the union of the boundaries of the pseudo-circles is a connected set.

Original entry on oeis.org

1, 1, 6, 112, 15528

Offset: 0

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

Arrangements in A288559 that are connected, in the sense that the union of the (boundaries of the) pseudo-circles is a connected set.
These counts have been reduced for mirror symmetry.
See A250001, the main entry for this problem, for further information.

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

A288562 Number of arrangements of n pseudo-circles in the affine plane with the property that every pseudo-circle intersects all the other circles.

Original entry on oeis.org

1, 1, 1, 4, 45, 5108, 4598809

Offset: 0

N. J. A. Sloane, Jun 12 2017, based on information supplied by Jon Wild on Aug 31 2016

Arrangements in A288559 that are connected, with the property that every pseudo-circle intersects all the other pseudo-circles.
These counts have been reduced for mirror symmetry.
See A250001, the main entry for this problem, for further information.

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

a(6) from Manfred Scheucher, May 09 2018

A288564 Number of connected one-sided arrangements of n pseudo-circles in the affine plane, in the sense that the union of the solid pseudo-circles is a connected set.

Original entry on oeis.org

1, 1, 2, 11, 183, 30408

Offset: 0

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

Arrangements in A288563 that are connected (in the sense that the union of the solid pseudo-circles is a connected set).
These counts have not been reduced for mirror symmetry.
See A250001, the main entry for this problem, for further information.

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

A288565 Number of connected one-sided arrangements of n pseudo-circles in the affine plane, in the sense that the union of the boundaries of the pseudo-circles is a connected set.

Original entry on oeis.org

1, 1, 1, 6, 139, 28643

Offset: 0

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

Arrangements in A288559 that are connected, in the sense that the union of the (boundaries of the) pseudo-circles is a connected set.
These counts have not been reduced for mirror symmetry.
See A250001, the main entry for this problem, for further information.

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

A288567 Number of connected arrangements of n circles in the affine plane, in the sense that the union of the boundaries of the circles is a connected set and every circle intersects all the other circles.

Original entry on oeis.org

1, 1, 1, 3, 21, 980

Offset: 0

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

These counts have been reduced for mirror symmetry.

See A250001, the main entry for this problem, for further information.

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

cp's OEIS Frontend

A383744 The number of distinct straightedge-and-compass constructions that can be made with a total of n lines and circles up to rigid motion.

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A288555 Number of one-sided arrangements of n circles in the affine plane.

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A288556 Number of connected one-sided arrangements of n circles in the affine plane, in the sense that the union of the solid circles is a connected set.

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A288557 Number of connected one-sided arrangements of n circles in the affine plane, in the sense that the union of the boundaries of the circles is a connected set.

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A288560 Number of connected arrangements of n pseudo-circles in the affine plane, in the sense that the union of the solid pseudo-circles is a connected set.

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A288561 Number of connected arrangements of n pseudo-circles in the affine plane, in the sense that the union of the boundaries of the pseudo-circles is a connected set.

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A288562 Number of arrangements of n pseudo-circles in the affine plane with the property that every pseudo-circle intersects all the other circles.

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A288564 Number of connected one-sided arrangements of n pseudo-circles in the affine plane, in the sense that the union of the solid pseudo-circles is a connected set.

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A288565 Number of connected one-sided arrangements of n pseudo-circles in the affine plane, in the sense that the union of the boundaries of the pseudo-circles is a connected set.

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Comments

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A288567 Number of connected arrangements of n circles in the affine plane, in the sense that the union of the boundaries of the circles is a connected set and every circle intersects all the other circles.

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Author

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Comments

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