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

1,2

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

Table of n, a(n) for n=1..28.

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.

Sequence in context: A287488 A320434 A329394 * A209284 A321468 A288044

Adjacent sequences: A057781 A057782 A057783 * A057785 A057786 A057787

Keyword

nonn,nice,hard,more

Author

N. J. A. Sloane, Nov 04 2000

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

Status

approved