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A342537 Number of free polyominoes with n cells having simply-connected interiors. 4

%I #14 Jan 04 2023 11:55:00

%S 1,1,2,5,12,35,108,368,1283,4639,17003,63222,236819,893515,3387953,

%T 12904855,49335965,189243115

%N Number of free polyominoes with n cells having simply-connected interiors.

%C The polyominoes referred to in the definition are those having a single traceable perimeter. The definition therefore includes the heptomino with a hole, as in this case the border, although not self-avoiding (it meets itself at a corner) is still traceable; it excludes the square octomino with a hole, whose border consists of two distinct polygons. Thus starting from n=8, A000104(n) < a(n) < A000105(n).

%Y Cf. A000104 (free polyominoes without holes), A000105 (free polyominoes).

%K nonn,more

%O 1,3

%A _John Mason_, _Allan C. Wechsler_, Mar 15 2021

%E a(17)-a(18) from _John Mason_, Jan 04 2023

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Last modified February 27 05:55 EST 2024. Contains 370362 sequences. (Running on oeis4.)