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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A056842 Number of polydrafters: a(n) is the number of polydrafters with n cells.

Original entry on oeis.org

1, 6, 14, 64, 237, 1024, 4254, 18664, 81865, 365190, 1634801, 7388372
Offset: 1

Views

Author

James Sellers, Aug 28 2000

Keywords

Comments

See the Paterson link for the definition.
Restatement of the definition: A polydrafter is a polygon formed by joining 30-60-90 triangles, according to the following rules:
(a) Two triangles may be joined along their short legs, with their right angles touching;
(b) Two triangles may be joined along their long legs, with their right angles touching;
(c) Two triangles may be joined along their hypotenuses, in either direction;
(d) The short leg of triangle 1 may be joined to half of the hypotenuse of triangle 2, with the right angle of triangle 1 touching the midpoint of the hypotenuse of triangle 2.

Examples

			a(3) = 14 because there are 14 tridafters. The second Vicher link shows various arrangements of them.

References

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

Links

Crossrefs

Cf. A217720 (number of one-sided polydrafters with n cells).
Cf. A289137 (number of extended [two-sided] polydrafters with n cells).

Extensions

Edited by David Wasserman, Dec 01 2003
a(10) from George Sicherman, Jun 23 2020
a(11)-a(12) from Aaron N. Siegel, May 13 2022

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.

Links

Crossrefs

Cf. A056842, A217720, A289137.
Showing 1-2 of 2 results.

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