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

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

Offset

1,2

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.

References

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

Links

Table of n, a(n) for n=1..12.

D. Paterson, Pentominos & Dodecadudes

M. Vicher, Polyforms

M. Vicher, Tridrafters

Eric Weisstein's World of Mathematics, Polydrafter.

Example

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

Crossrefs

Cf. A217720 (number of one-sided polydrafters with n cells).

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

Sequence in context: A252541 A333103 A139257 * A182752 A200033 A219376

Adjacent sequences: A056839 A056840 A056841 * A056843 A056844 A056845

Keyword

nonn,more,hard

Author

James A. Sellers, Aug 28 2000

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

Status

approved