A387209 Number of convex polygons with perimeter n on the regular triangular lattice, not counting rotations and reflections as distinct.

0, 0, 0, 1, 1, 1, 3, 2, 4, 4, 6, 5, 10, 7, 12, 11, 16, 13, 22, 17, 26, 23, 32, 27, 41, 33, 47, 42, 56, 48, 68, 57, 77, 69, 89, 78, 105, 90, 117, 106, 133, 118, 153, 134, 169, 154, 189, 170, 214, 190, 234, 215, 259, 235, 289, 260, 314, 290, 344, 315, 380

Offset: 0

Author

Walter Trump, Aug 22 2025

Keywords

• nonn
• new

Comments

a(n) also is the number of convex polyiamonds (triangular polyominoes) with perimeter n.

Links

• Walter Trump, Table of n, a(n) for n = 0..10000
• Walter Trump, Convex Polyiamonds
• Walter Trump, Examples for a(3)-a(12)

Crossrefs

Cf. A096004 (number of convex polyiamonds with n cells), A284869 (including nonconvex but simply connected polyiamonds with perimeter n), A057729 (including polyiamonds with holes), A036418 (including rotations and reflections but no holes).