A341219 Number of well-connected free polyominoes with n cells, where a polyomino is defined as well-connected if, for all the squares it contains, the removal of that single square would result in an intact polyomino.

1, 1, 1, 0, 1, 0, 1, 0, 3, 1, 6, 2, 25, 18, 88

Offset

0,9

Comments

Examples of well-connected polyominoes are rectangles and loops:

.

XXXX

XXXX (rectangle)

.

XXX

X X (loop)

XXX

Links

Table of n, a(n) for n=0..14.

John Mason, Well connected polyominoes

Example

a(4) = 1 because the 2 X 2 square polyomino is the only tetromino to be well-connected. The removal of any single square always results in an intact tromino. In each of the other 4 tetrominoes, there is a square whose removal would result in something that is not an intact polyomino.

Crossrefs

Cf. A000105.

Sequence in context: A322387 A336173 A072361 * A145366 A145367 A124928

Adjacent sequences: A341216 A341217 A341218 * A341220 A341221 A341222

Keyword

nonn,more

Author

John Mason, Feb 07 2021

Status

approved