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A006749 Number of asymmetric polyominoes with n cells.
(Formerly M3906)
26
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
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...
FORMULA
a(n) + A259090(n) = A000105(n). - R. J. Mathar, Sep 29 2021
CROSSREFS
Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554.
Sequence in context: A292760 A270322 A056884 * A002213 A099949 A006231
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
Extended to n=28 by Tomás Oliveira e Silva.
STATUS
approved

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Last modified February 27 08:19 EST 2024. Contains 370367 sequences. (Running on oeis4.)