A103465 Number of polyominoes that can be formed from n regular unit pentagons (or polypents of order n).

1, 1, 2, 7, 25, 118, 551, 2812, 14445, 76092, 403976, 2167116, 11698961, 63544050, 346821209, 1901232614

Offset

1,3

Comments

Number of 5-polyominoes with n pentagons. A k-polyomino is a non-overlapping union of n regular unit k-gons.

Unlike A051738, these are not anchored polypents but simple polypents. - George Sicherman, Mar 06 2006

Polypents (or 5-polyominoes in Koch and Kurz's terminology) can have holes and this enumeration includes polypents with holes. - George Sicherman, Dec 06 2007

Links

Table of n, a(n) for n=1..16.

Erich Friedman, Math Magic, September and November 2004.

Matthias Koch and Sascha Kurz, Enumeration of generalized polyominoes (preprint) arXiv:math.CO/0605144

Sascha Kurz, k-polyominoes.

George Sicherman, Catalogue of Polypents, at Polyform Curiosities.

Example

a(3)=2 because there are 2 geometrically distinct ways to join 3 regular pentagons edge to edge.

Crossrefs

Cf. A103465, A103466, A103467, A103468, A103469, A103470, A103471, A103472, A103473, A120102, A120103, A120104.

Cf. A000105, A000577, A000228.

Sequence in context: A150535 A076176 A188719 * A103464 A358498 A339515

Adjacent sequences: A103462 A103463 A103464 * A103466 A103467 A103468

Keyword

more,nonn

Author

Sascha Kurz, Feb 07 2005; definition revised and sequence extended Apr 12 2006 and again Jun 09 2006

Extensions

Entry revised by N. J. A. Sloane, Jun 18 2006

Status

approved