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Non-polyominoes are figures (like polyominoes), but are orthogonally connected at least in one vertex. So this number is equal to number of (free) n-polyplets minus number of free polyominoes: a(n) = A030222(n) - A000105(n).
Table of n, a(n) for n=1..17.
Eric W. Weisstein, MathWorld: Polyplet
XX...X.X..X.. (the 3 for n=3)
a(3) = 5 - 2 = 3
a(4) = 22 - 5 = 17
a(5) = 94 - 12 = 82
Cf. A030222, A000105, A006770 (fixed polyplets), A001168 (fixed polyominoes).
Sequence in context: A164305 A202247 A225342 * A217623 A083217 A225307
Adjacent sequences: A194593 A194594 A194595 * A194597 A194598 A194599
Jani Melik, Aug 30 2011