A268427 Number of distinct free polyominoes that will fit in a square of size n X n.

1, 4, 35, 1280, 263374, 205666062

Offset

1,2

Comments

A268416 gives the number of polyominoes that fill fit inside an n X n square, but with the restriction that they have their edges aligned with the sides of the square. The current sequence removes that restriction, and hence differs from A268416 at a(5). See link "Explanation of a(5)".

Links

Table of n, a(n) for n=1..6.

John Mason, Explanation of a(5)

Talmon Silver, Computing a(6)

Example

For n = 2, the four polyominoes are the 1 X 1, 1 X 2, and 2 X 2 squares or rectangles, and the 3-celled L-shape. - N. J. A. Sloane, Jan 21 2021

Crossrefs

Cf. A000105 (free polyominoes), A268416, A339848.

Sequence in context: A076818 A005026 A268416 * A123745 A183882 A053426

Adjacent sequences: A268424 A268425 A268426 * A268428 A268429 A268430

Keyword

nonn,more

Author

John Mason, Feb 04 2016

Extensions

A value for a(6) was submitted by Sam Vodovoz on Aug 02 2020 but this was retracted via email on Aug 03 2020. - N. J. A. Sloane, Aug 03 2020

a(5) corrected by Talmon Silver, Sep 24 2020

a(6) from Talmon Silver, Oct 01 2020

Added "free" to definition. - N. J. A. Sloane, Jan 21 2021

Status

approved