1,4

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.

Wikipedia, Polyomino.

Wikipedia, Eulerian path.

The one 3-cell polyomino:

+---+---+

| | |

+---+---+

| |

+---+

The two 4-cell polyominoes:

+---+---+---+ +---+---+

| | | | | | |

+---+---+---+ +---+---+---+

| | | | |

+---+ +---+---+

The three 5-cell polyominoes:

+---+---+ +---+ +---+---+

| | | | | | | |

+---+---+---+ +---+---+---+ +---+---+---+

| | | | | | | | | |

+---+---+ +---+---+---+ +---+---+

| | | | | |

+---+ +---+ +---+

Cf. A000105, A268311, A245620.

Sequence in context: A327018 A329128 A368687 * A103065 A281142 A110448

Adjacent sequences: A330439 A330440 A330441 * A330443 A330444 A330445

nonn,more

Scott R. Shannon, Dec 14 2019

approved