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A038119 Number of n-celled solid polyominoes (or free polycubes, allowing mirror-image identification).
(Formerly M1760)
33
1, 1, 2, 7, 23, 112, 607, 3811, 25413, 178083, 1279537, 9371094, 69513546, 520878101, 3934285874, 29915913663 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
A000162 but with one copy of each mirror-image deleted.
From R. J. Mathar, Mar 19 2018: (Start)
We can split the numbers into an irregular table which lists in row n how many configurations have c contacts for c >= 0:
1;
0 1;
0 0 2;
0 0 0 6 1;
0 0 0 0 21 2;
0 0 0 0 0 91 19 2;
0 0 0 0 0 0 484 110 12 1;
0 0 0 0 0 0 0 2817 852 129 12 0 1;
0 0 0 0 0 0 0 0 17788 6321 1166 132 5 1;
Row lengths are 1+A007818(n). Row sums are a(n).
(End)
Number of unoriented polyominoes with n cubical cells of the regular tiling with Schläfli symbol {4,3,4}. For unoriented polyominoes, chiral pairs are counted as one.- Robert A. Russell, Mar 21 2024
REFERENCES
Computed by Achim Flammenkamp.
S. W. Golomb, Polyominoes. Scribner's, NY, 1965; second edition (Polyominoes: Puzzles, Packings, Problems and Patterns) Princeton Univ. Press, 1994.
W. F. Lunnon, Symmetry of cubical and general polyominoes, pp. 101-108 of R. C. Read, editor, Graph Theory and Computing. Academic Press, NY, 1972.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Achim Flammenkamp, Home page
Kevin L. Gong, Polyominoes Home Page.
FORMULA
a(n) = A000162(n) - A371397(n) = A371397(n) + A007743(n)). - Robert A. Russell, Mar 21 2024
MATHEMATICA
A[s_Integer] := With[{s6 = StringPadLeft[ToString[s], 6, "0"]}, Cases[ Import["https://oeis.org/A" <> s6 <> "/b" <> s6 <> ".txt", "Table"], {_, _}][[All, 2]]];
A000162 = A@000162;
A007743 = A@007743;
a[n_] := (A007743[[n]] + A000162[[n]])/2;
a /@ Range[16] (* Jean-François Alcover, Jan 16 2020 *)
CROSSREFS
32nd row of A366766.
Cf. A000162 (oriented), A371397 (chiral), A007743 (achiral), A001931 (fixed).
Sequence in context: A265797 A150388 A073344 * A006986 A000903 A049021
KEYWORD
nonn,hard,more,nice,changed
AUTHOR
EXTENSIONS
More terms from Brendan Owen (brendan_owen(AT)yahoo.com), Jan 02 2002
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 05 2007
STATUS
approved

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Last modified March 29 04:59 EDT 2024. Contains 371264 sequences. (Running on oeis4.)