A006749 Number of asymmetric polyominoes with n cells.

0, 0, 0, 1, 5, 20, 84, 316, 1196, 4461, 16750, 62878, 237394, 899265, 3422111, 13069026, 50091095, 192583152, 742560511, 2870523142, 11122817672, 43191285751, 168046076423, 654997492842, 2557223459805, 9999080270766, 39152997087077, 153511067364760

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice

Comments

This sequence counts polyominoes whose symmetry group has order 1.

References

• A. R. Conway and A. J. Guttmann, On two-dimensional percolation, J. Phys. A: Math. Gen. 28(1995) 891-904.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• John Mason, Table of n, a(n) for n = 1..50 (This version corrects erroneous values from a(44) onwards in previous version.)
• Tomás Oliveira e Silva, Enumeration of polyominoes
• T. R. Parkin, L. J. Lander, and D. R. Parkin, Polyomino Enumeration Results, presented at SIAM Fall Meeting, 1967, and accompanying letter from T. J. Lander (annotated scanned copy). See page 21.
• D. H. Redelmeier, Counting polyominoes: yet another attack, Discrete Math., 36 (1981), 191-203.
• D. H. Redelmeier, Table 3 of Counting polyominoes...

Crossrefs

Cf. A000105, A001168, A006746, A056877, A006748, A056878, A006747, A006749.

Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554.

Formula

a(n) + A259090(n) = A000105(n). - R. J. Mathar, Sep 29 2021

Extensions

Extended to n=28 by Tomás Oliveira e Silva.