A006770 Number of fixed n-celled polyominoes which need only touch at corners. (Formerly M3565)

1, 4, 20, 110, 638, 3832, 23592, 147941, 940982, 6053180, 39299408, 257105146, 1692931066, 11208974860, 74570549714, 498174818986, 3340366308393, 22471158811164

Offset

1,2

Comments

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

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

Table of n, a(n) for n=1..18.

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. See also the associated code repository.

Eric Weisstein's World of Mathematics, Polyplet.

Wikipedia, Pseudo polyomino

Example

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

Crossrefs

Cf. A030222 (free polyplets).

10th row of A366767.

Sequence in context: A271932 A153295 A380684 * A158827 A393005 A263854

Adjacent sequences: A006767 A006768 A006769 * A006771 A006772 A006773

Keyword

nonn,hard,more

Author

N. J. A. Sloane

Extensions

One more term from Joseph Myers, Sep 26 2002

a(18) from Tremblay and Vernay added by Andrei Zabolotskii, Dec 02 2025

Status

approved