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A103465 Number of polyominoes that can be formed from n regular unit pentagons (or polypents of order n). 13
1, 1, 2, 7, 25, 118, 551, 2812, 14445, 76092, 403976, 2167116, 11698961, 63544050, 346821209, 1901232614 (list; graph; refs; listen; history; text; internal format)



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


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

S. Kurz, k-polyominoes.

G. L. Sicherman, Catalogue of Polypents, at Polyform Curiosities.


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


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

Cf. A000105, A000577, A000228.

Sequence in context: A150535 A076176 A188719 * A103464 A339515 A323658

Adjacent sequences:  A103462 A103463 A103464 * A103466 A103467 A103468




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


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

Corrected the dates of the Math Magic pages under "Links." George Sicherman, Nov 08 2009



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Last modified June 26 18:18 EDT 2022. Contains 354885 sequences. (Running on oeis4.)