A300697 Volumes of concertina hypercubes.

0, 2, 8, 52, 472, 5526, 79384, 1352744, 26684928

Offset

0,2

Comments

A concertina n-cube is a truncation of an n-cube with edge length n+1. Its volume is an even integer. (The values divided by 2 are in A300698.)

Links

Table of n, a(n) for n=0..8.

Tilman Piesk, Formulas in predicate logic (Wikiversity).

Tilman Piesk, Transparent and solid image of a concertina cube.

Tilman Piesk, Python code used to generate the sequence.

Example

Dimension n                     1,  2,   3,   4,    5,      6
Hypercube volume A000169(n+1)   2,  9,  64, 625, 7776, 117649
Cut away volume                 0,  1,  12, 153, 2250,  38265
Remaining volume a(n)           2,  8,  52, 472, 5526,  79384
Example for dimension 3: The initial cube has edge length 4 and thus a volume of 64. The volume cut away is 12, so the remaining concertina cube has a volume of 52.

Crossrefs

Cf. A300698, A000169.

Sequence in context: A111088 A367371 A006351 * A277499 A089467 A195192

Adjacent sequences: A300694 A300695 A300696 * A300698 A300699 A300700

Keyword

nonn,more

Author

Tilman Piesk, Mar 11 2018

Extensions

a(7)-a(8) from Ludovic Schwob, Jan 02 2025

Status

approved