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a(n) is the number of almost unitary polyominoes of size n. An almost unitary polyomino is one in which all but 1 of its perimeter walls have length 1.
1

%I #10 May 01 2023 10:01:46

%S 0,0,0,1,0,0,2,2,1,6,9,11,21,49,69,117,249,427

%N a(n) is the number of almost unitary polyominoes of size n. An almost unitary polyomino is one in which all but 1 of its perimeter walls have length 1.

%H George Sicherman, <a href="https://sicherman.net/nunitary/nunitarya.html">Catalogue of Almost Unitary Polyominoes</a>

%e a(4)=1 because of:

%e O

%e OO

%e O

%Y Cf. A245660, A362709.

%K nonn,hard,more

%O 1,7

%A _John Mason_, Apr 30 2023