A330442 The number of free polyominoes with n cells which, when drawn on a 2D square grid, contain an Eulerian path.

1, 1, 1, 2, 3, 6, 8, 18

Offset: 1

Author

Scott R. Shannon, Dec 14 2019

Keywords

• nonn
• more

Comments

a(n) is the total number of free polyominoes containing n cells which, when drawn on a 2D square grid, contain an Eulerian path. Such polyominoes must have all edges of length one, see A245620, have one or two edges of length two with all other edges of length one, or else have one edge of length three with all other edges of length one. These edges also include those bordering internal holes.

Examples

			The one 3-cell polyomino:
  +---+---+
  |   |   |
  +---+---+
      |   |
      +---+
The two 4-cell polyominoes:
  +---+---+---+    +---+---+
  |   |   |   |    |   |   |
  +---+---+---+    +---+---+---+
      |   |            |   |   |
      +---+            +---+---+
The three 5-cell polyominoes:
  +---+---+            +---+        +---+---+
  |   |   |            |   |        |   |   |
  +---+---+---+    +---+---+---+    +---+---+---+
      |   |   |    |   |   |   |        |   |   |
      +---+---+    +---+---+---+        +---+---+
      |   |            |   |                |   |
      +---+            +---+                +---+
		

Links

• Wikipedia, Polyomino.
• Wikipedia, Eulerian path.

Crossrefs

Cf. A000105, A268311, A245620.