A393992 - OEIS

A393992

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

0, 1, 3, 6, 8, 13, 17, 23, 29, 36, 43, 51, 60, 69, 81, 92, 106, 119, 134, 149, 166, 182, 200

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..23.

Pontus von Brömssen, Illustration of all optimal polyominoes for 1 <= n <= 23.

Pontus von Brömssen, Illustration of the unique polyomino with 6 cells and a(6)=13 lines.

Pontus von Brömssen, Illustration of the unique polyomino with 13 cells and a(13)=60 lines.

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 <= 4 = A380991(2). The first part is equivalent to n*(n-1)/2 - a(n) being nondecreasing.

CROSSREFS

Cf. A000105, A380991, A393939, A393993 (distinct slopes), A394392 (number of optimal polyominoes), A394394 (polycubes).

Sequence in context: A219730 A373083 A337484 * A139001 A396811 A090961

Adjacent sequences: A393989 A393990 A393991 * A393993 A393994 A393995

KEYWORD

nonn,more

AUTHOR

Pontus von Brömssen, Mar 09 2026

STATUS

approved