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

Author

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

Keywords

• more
• nonn

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

Examples

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

Links

• 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.

Crossrefs

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

Cf. A000105, A000577, A000228.

Extensions

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