A393969 a(n) is the number of distinct n-edges, fully-dimensional incomplete open cubes (see Comments for precise definition).

3, 5, 14, 24, 32, 25, 13, 5, 1

Offset

3,1

Comments

Here, an incomplete open cube is a fully connected proper subset of the edges of a cube, with the additional requirement that each of the three coordinate directions is parallel to at least one edge of the object. Two configurations are considered identical if one can be obtained from the other by rotation.

The 122 resulting total configurations are the subject of Sol DeWitt's 1974 work "Incomplete Open Cubes".

Links

Table of n, a(n) for n=3..11.

Paul Dancstep, Exploration & Epiphany, 3Blue1Brown YouTube video, 2025.

Sol DeWitt, Incomplete Open Cubes, 1974, San Francisco Museum of Modern Art.

Alison Pitt, An Exploration of Incomplete Open Cubes, 2023.

Natasha Rozhkovskaya and Michael Reb, Is the List of Incomplete Open Cubes Complete?, Nexus Network Journal, Volume 17, 2015, pp. 913-925.

Crossrefs

Cf. A222186, A222192, A383799, A393693.

Sequence in context: A026645 A026667 A372436 * A295359 A104208 A378262

Adjacent sequences: A393966 A393967 A393968 * A393970 A393971 A393972

Keyword

nonn,fini,full

Author

Paolo Xausa, Mar 31 2026

Status

approved