1,3

A slope is counted only once, even if there are several parallel lines with that slope.

Pontus von Brömssen, Illustration of all optimal polyominoes for 1 <= n <= 18.

Index entries for sequences related to polyominoes.

For n >= 3, a(n) >= n + max{A331781(k,n-1-k); 1<=k<=n-2}, realized by the polyomino with cell centers in (0,0), (x,1) for 0 <= x <= k, and (1,y) for 2 <= y <= n-k-1, for an optimal value of k. Does equality hold for all n >= 3?

Cf. A000105, A331781, A393992 (distinct lines), A393994 (polycubes), A394393 (number of optimal polyominoes).

Sequence in context: A256698 A024182 A301752 * A173339 A064269 A260485

Adjacent sequences: A393990 A393991 A393992 * A393994 A393995 A393998

nonn,more

Pontus von Brömssen, Mar 09 2026

approved