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%I #42 Mar 23 2023 16:45:04
%S 1,1,2,4,11,27,83,255,847,2829,9734,33724,118245,416816,1478602,
%T 5267171,18840144,67611472,243378415,878407170,3178068821,11523323634,
%U 41865833602,152382134767
%N a(n) is the number of n-celled polyominoes with perimeter 2n+2.
%C 2n+2 is the maximal perimeter of an n-celled polyomino. a(n) is the number of n-celled polyominoes that have a tree as their connectedness graph (vertices of this graph correspond to cells and two vertices are connected if the corresponding cells have a common edge).
%H Andrew Clarke, <a href="http://www.recmath.com/PolyPages/PolyPages/index.htm?Isopolyos.html">Isoperimetrical Polyominoes</a>, The Poly Pages.
%H Herman Tulleken, <a href="https://www.researchgate.net/publication/333296614_Polyominoes">Polyominoes 2.2: How they fit together</a>, (2019).
%F a(n) <= A000105(n), a(n) <= A057730(n+1).
%F a(n) >= A000602(n) [see comment on edge graph trees]. - _R. J. Mathar_, Mar 08 2021
%Y Cf. A000105, A057730. Diagonal of A342243.
%Y A359522 counts only polyominoes with holes.
%Y A002013 counts only unbranched polyominoes.
%Y A038142 is the analog for polyhexes.
%K hard,more,nonn
%O 1,3
%A _Tanya Khovanova_, Jul 27 2007
%E a(14)-a(16) from _David Radcliffe_, Dec 25 2017
%E a(17) from _David Radcliffe_, Dec 26 2017
%E a(18)-a(24) from _John Mason_, Dec 11 2021
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