A048663 Number of rooted polycubes with n cells, with no symmetries removed.

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

Table of n, a(n) for n=1..19.

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

Adjacent sequences: A048660 A048661 A048662 * A048664 A048665 A048666

Keyword

nonn

Author

Richard C. Schroeppel, Dan Hoey

Extensions

a(12)-a(19) from Andrew Howroyd, Dec 04 2018

Status

approved