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Number of distinct free polyominoes that fit in an n X n square but are not a proper sub-polyomino of any polyomino that fits in the square.
1

%I #25 Jan 21 2021 12:27:34

%S 1,1,1,1,3,6,16,27,44,70

%N Number of distinct free polyominoes that fit in an n X n square but are not a proper sub-polyomino of any polyomino that fits in the square.

%C A polyomino A is a proper sub-polyomino of B if one or more cells can be added to A to form B.

%C Except for the n X n polyomino that fills the square all of the other polyominos must have their edges aligned at an angle to the sides of the square.

%C This counts the minimum subset of polyominoes needed to produce A268427 - that sequence counts the sub-polyominoes of this sequence.

%H John Mason, <a href="/A268427/a268427_1.pdf">Explanation of a(5)</a>

%H Talmon Silver, <a href="/A268427/a268427_2.pdf">Computing a(6)</a>

%H Talmon Silver, <a href="https://drive.google.com/drive/folders/1AJJ8uhgdHhmpb-IKf_MLsIZgqXLD-Bth">Programs</a>

%e For n=1, 2, 3, 4 the only polyominoes are the n X n polyominoes. Thus, a(1)=a(2)=a(3)=a(4)=1.

%e For n=5 and n=6 all of the other polyominoes are shown in the links.

%Y Cf. A268427.

%K nonn,more

%O 1,5

%A _Talmon Silver_, Dec 19 2020