A354308 Number of free polyjogs with n cells.

1, 1, 4, 17, 88, 503, 3071, 19372, 124575, 813020, 5361539, 35662727, 238864272, 1609398564

Offset: 1

Author

Aaron N. Siegel, May 23 2022

Keywords

• nonn
• hard
• more

Comments

A polyjog is a polyform composed of n connected unit squares adjoined along half-edges: every pair of adjacent cells shares an edge of length exactly 1/2. The polyjogs of order n form a subset of polyominoes of order 4n.

Figures that differ by a rotation or reflection are considered equivalent.

It is not hard to prove that every polyjog can be tiled by unit squares in exactly one way. Therefore, equivalences involving internal rearrangement of unit squares are not relevant (unlike related sequences; cf. A216583).

Examples

			a(3) = 4, because there are four ways to adjoin three unit squares by half-edges:
aa  cc     cc  aa      aa
aabbcc  aa cc  aabb    aa
  bb    aabb     bbcc   bb
          bb       cc   bbcc
                          cc
(In these figures, the three unit squares are depicted by 2 X 2 arrangements of letters a, b, and c.)
		

Links

• George Sicherman, Catalogue of Polyjogs

Crossrefs

Cf. A000105, A216583.