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A048663
Number of rooted polycubes with n cells, with no symmetries removed.
8
1, 6, 45, 344, 2670, 20886, 164514, 1303304, 10375830, 82947380, 665440039, 5354470860, 43196001173, 349254823554, 2829388506690, 22961191276080, 186622811691276, 1518914831183982, 12377727000122043
OFFSET
1,2
COMMENTS
"Rooted" means some cell of the polycube is designated as the origin. This has the effect of multiplying the count by the volume of the polycube.
REFERENCES
Dan Hoey, Bill Gosper and Richard C. Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999.
LINKS
R. C. Schroeppel, A few mathematical experiments, Experimental Mathematics Workshop, Oakland, 2004.
FORMULA
a(n) = n * A001931(n). - Andrew Howroyd, Dec 04 2018
EXAMPLE
There are six dicubes, each consisting of the origin cube together with one adjacent cube, in each of the six directions.
MATHEMATICA
A001931 = Cases[Import["https://oeis.org/A001931/b001931.txt", "Table"], {_, _}][[All, 2]];
a[n_] := n * A001931[[n]];
Array[a, 19] (* Jean-François Alcover, Sep 13 2019 *)
CROSSREFS
A row of the array in A048790.
Cf. A001931.
Sequence in context: A189801 A024077 A097129 * A095003 A004988 A257633
KEYWORD
nonn
AUTHOR
Richard C. Schroeppel, Dan Hoey
EXTENSIONS
a(12)-a(19) from Andrew Howroyd, Dec 04 2018
STATUS
approved