A006770 Number of fixed n-celled polyominoes which need only touch at corners.

1, 4, 20, 110, 638, 3832, 23592, 147941, 940982, 6053180, 39299408, 257105146, 1692931066, 11208974860, 74570549714, 498174818986, 3340366308393

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• more

Comments

Also known as fixed polyplets. - David Bevan, Jul 28 2009

Examples

			a(2)=4: the two fixed dominoes and the two rotations of the polyplet consisting of two cells touching at a vertex. - _David Bevan_, Jul 28 2009
a(3)=20 counts 4 rotations (by 0°, 45°, 90°, 135°) of the straight ... trinomino, and 8 rotations (by multiples of 45°) of the L-shaped .: trinomino and the ..· 3-polyplet, cf. link to the image. - _M. F. Hasler_, Sep 30 2014
		

References

• D. H. Redelmeier, personal communication.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• M. F. Hasler, Illustration of the A006770(3)=20 fixed 3-polyplets, Sep 29 2014.
• S. Mertens, Lattice animals: a fast enumeration algorithm and new perimeter polynomials, J. Stat. Phys. 58 (5-6) (1990) 1095-1108, Table 1.
• H. Redelmeier, Emails to N. J. A. Sloane, 1991
• Hugo Tremblay and Julien Vernay, On the generation of discrete figures with connectivity constraints, RAIRO-Theor. Inf. Appl. (2024) Vol. 58, Art. No. 16. See p. 13.
• Eric Weisstein's World of Mathematics, Polyplet.
• Wikipedia, Pseudo polyomino

Crossrefs

Cf. A030222 (free polyplets).

10th row of A366767.

Extensions

One more term from Joseph Myers, Sep 26 2002