A354308 Number of free polyjogs with n cells.

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

Offset

1,3

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).

Links

Table of n, a(n) for n=1..14.

George Sicherman, Catalogue of Polyjogs

Example

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.)

Crossrefs

Cf. A000105, A216583.

Sequence in context: A114190 A135168 A364212 * A357617 A350474 A058279

Adjacent sequences: A354305 A354306 A354307 * A354309 A354310 A354311

Keyword

nonn,hard,more

Author

Aaron N. Siegel, May 23 2022

Status

approved