A394394 Largest number of distinct lines determined by pairs of cell centers of a polycube with n cells.

0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 349, 376, 404, 433, 463, 492, 524, 557, 591, 626, 662, 699, 737, 776

Offset

1,3

Links

Table of n, a(n) for n=1..40.

Pontus von Brömssen, Illustration of the unique free polycube with 26 cells and no 3 collinear cells.

Index entries for sequences related to polyominoes.

Formula

a(n+1)-n <= a(n) <= n*(n-1)/2, with equality in the second part if and only if n <= 26 = largest k such that A393938(k,2) > 0. The first part is equivalent to n*(n-1)/2 - a(n) being nondecreasing.

Crossrefs

Cf. A038119, A393938, A393939 (number of optimal polycubes), A393992 (polyominoes), A393994 (distinct directions of lines).

Sequence in context: A105336 A130910 A105337 * A105338 A105339 A089594

Adjacent sequences: A394391 A394392 A394393 * A394395 A394396 A394397

Keyword

nonn,more

Author

Pontus von Brömssen, Mar 19 2026

Status

approved