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

0,7

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).

Sequence in context: A059851 A327637 A366409 * A385348 A345082 A047993

Adjacent sequences: A387206 A387207 A387208 * A387210 A387211 A387212

Keyword

nonn

Author

Walter Trump, Aug 22 2025

Status

approved