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 1-5 of 5 results.

A217720 Number of one-sided polydrafters with n cells.

Original entry on oeis.org

2, 8, 28, 116, 474, 2001, 8508, 37162, 163730, 729683, 3269602, 14773831
Offset: 1

Views

Author

George Sicherman, Mar 21 2013

Keywords

Comments

A polydrafter is a plane figure formed by joining equal triangles with angles of 30, 60, and 90 degrees with certain restrictions on how they are joined. See A056842 for details. One-sided means that distinct mirror images are counted separately.
For odd n, an n-drafter cannot have mirror symmetry, so odd entries in this sequence are double those in A056842.

Examples

			There are 6 two-sided didrafters, two have distinct mirror images, so there are 8 one-sided didrafters. Thus a(2) = 8.
		

References

  • Ed Pegg, Jr., Polyform puzzles, in Tribute to a Mathemagician, Peters, 2005, pp. 119-125.

Crossrefs

Cf. A056842 (number of two-sided polydrafters).

Extensions

a(8)-a(12) from Aaron N. Siegel, May 13 2022

A289137 Number of extended polydrafters with n cells, identifying mirror images.

Original entry on oeis.org

1, 13, 88, 1025, 11822, 147003, 1866907
Offset: 1

Views

Author

George Sicherman, Jun 25 2017

Keywords

Comments

An extended polydrafter is a plane figure formed by joining congruent 30-60-90 triangles along edges and half hypotenuses, without the requirement for proper polydrafters that the cells lie on the polyiamond (triangle) grid.

Examples

			a(2)=13 because there are 6 proper didrafters and 7 more didrafters that do not conform to the polyiamond grid.
See the Logelium link for diagrams.
		

Crossrefs

Cf. A056842 (number of [proper] polydrafters with n cells); A217720 (number of one-sided polydrafters with n cells).

A056843 Number of polydudes(1): a(n) is the number of polydudes with n cells. See the first link for the source of this sequence. The definition is unknown. Not the same as A091130.

Original entry on oeis.org

0, 3, 1, 9, 15, 59, 152, 513, 1539, 4993, 15836
Offset: 1

Views

Author

James Sellers, Aug 28 2000

Keywords

Comments

The polydudes(1) (this sequence) and the polydudes(2) (A091130) are both subsets of the polydrafters (A056842).
Speculation about the definition: There are 3 2-drafters that have no 30-degree angles. It appears that all polydudes are unions of these 3 2-drafters. All the pictured 5-dudes and 6-dudes have this property and the numbers of n-drafters with this property agree with the first 5 terms. I believe there is only one 6-drafter with this property that is not in the picture. This one was probably excluded because it has a 30-degree external angle, which none of the other polydudes can fit into. I can't guess what other exclusions might occur for n > 6. (D.R.W.)

Examples

			The second link shows all 5-dudes and 6-dudes.
		

Crossrefs

Extensions

Edited by David Wasserman, Dec 19 2003

A091130 Number of polydudes(2): a(n) is the number of polydudes with n cells. See the link for the definition. Not the same as A056843.

Original entry on oeis.org

1, 0, 4, 5, 22
Offset: 1

Views

Author

David Wasserman, Dec 19 2003

Keywords

Comments

The polydudes(1) (A056843) and the polydudes(2) (this sequence) are both subsets of the polydrafters (A056842).

Crossrefs

A351684 Number of convex polydrafters with n cells. These are proper polydrafters, whose cells conform to the polyiamond grid. Mirror images are identified.

Original entry on oeis.org

1, 4, 3, 7, 7, 13, 9, 15, 9, 14, 12, 27, 19, 29, 26, 29, 20, 36, 26, 48, 42, 46, 44, 53, 32, 54, 49, 69, 62, 82, 58, 72, 60, 67, 73, 119, 85, 106, 99, 93, 85, 126, 100, 152, 132, 142, 125, 145, 107, 142, 147, 185, 161, 194, 146, 169, 160, 186, 192, 271, 195, 251, 209, 199, 207, 260, 230, 330, 272, 275, 255, 293
Offset: 1

Views

Author

George Sicherman, May 16 2022

Keywords

Comments

These are conforming polydrafters as in A056842, as defined by Ed Pegg. They do not include extended polydrafters. See the Logelium link.

Examples

			For n=2 there are 6 proper didrafters.  Four are convex:  the rectangle, the kite, the moniamond (equilateral triangle), and the monopons (30°-30°-120° triangle). Thus a(2) = 4.
		

Crossrefs

Showing 1-5 of 5 results.