A057784 Number of polypons with n cells.

1, 2, 2, 4, 4, 10, 13, 29, 47, 100, 181, 383, 738, 1539, 3087, 6419, 13135, 27402, 56779, 118876, 248384, 521850, 1096261, 2310793, 4874305, 10305560, 21810868, 46239224

Offset: 1

Author

N. J. A. Sloane, Nov 04 2000

Keywords

• nonn
• nice
• hard
• more

Comments

A polypon is a polyform made up of 30-30-120 triangles from the [3.12^2] Laves tiling, joined along their edges. Because that tiling contains hexagons formed as a union of six triangles, with the division of the hexagon having less symmetry than the hexagon on its own, some polypons can be divided into their constituent triangles in more than one way, and whether the division is significant affects the values of a(n) when n >= 18 is a multiple of 6. For the present sequence, the division into triangles is considered significant. - Joseph Myers, Oct 02 2011

References

• Computed by Brendan Owen.

Links

• Andrew Clarke, Other Polyforms
• Ed Pegg, Jr., Illustrations of polyforms
• Eric Weisstein's World of Mathematics, Polypon [From _Eric W. Weisstein_, Apr 24 2009]

Crossrefs

Cf. A355562, A151531, A151532, A151533.

Extensions

Link updated by William Rex Marshall, Dec 16 2009

a(21)-a(26) from Joseph Myers, Oct 02 2011

a(27)-a(28) from Sean A. Irvine, Jul 04 2022