A038119 Number of n-celled solid polyominoes (or free polycubes, allowing mirror-image identification). (Formerly M1760)

1, 1, 2, 7, 23, 112, 607, 3811, 25413, 178083, 1279537, 9371094, 69513546, 520878101, 3934285874, 29915913663

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)

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

Table of n, a(n) for n=1..16.

Achim Flammenkamp, Home page

Kevin L. Gong, Polyominoes Home Page.

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

A038119 = (A007743+A000162)/2, A007743 = 2*A038119 - A000162, A000162 = 2*A038119 - A007743.

Sequence in context: A265797 A150388 A073344 * A006986 A000903 A049021

Adjacent sequences: A038116 A038117 A038118 * A038120 A038121 A038122

Keyword

nonn,hard,more,nice

Author

N. J. A. Sloane

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