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

Author

Richard C. Schroeppel, Dan Hoey

Keywords

• nonn

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.

Examples

			There are six dicubes, each consisting of the origin cube together with one adjacent cube, in each of the six directions.
		

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.

Crossrefs

A row of the array in A048790.

Cf. A001931.

Programs

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 *)

Formula

a(n) = n * A001931(n). - Andrew Howroyd, Dec 04 2018

Extensions

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