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A131482 a(n) is the number of n-celled polyominoes with perimeter 2n+2. 9
1, 1, 2, 4, 11, 27, 83, 255, 847, 2829, 9734, 33724, 118245, 416816, 1478602, 5267171, 18840144, 67611472, 243378415, 878407170, 3178068821, 11523323634, 41865833602, 152382134767 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
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).
LINKS
Andrew Clarke, Isoperimetrical Polyominoes, The Poly Pages.
Herman Tulleken, Polyominoes 2.2: How they fit together, (2019).
FORMULA
a(n) <= A000105(n), a(n) <= A057730(n+1).
a(n) >= A000602(n) [see comment on edge graph trees]. - R. J. Mathar, Mar 08 2021
CROSSREFS
Cf. A000105, A057730. Diagonal of A342243.
A359522 counts only polyominoes with holes.
A002013 counts only unbranched polyominoes.
A038142 is the analog for polyhexes.
Sequence in context: A319616 A148130 A350030 * A234845 A148131 A234844
KEYWORD
hard,more,nonn
AUTHOR
Tanya Khovanova, Jul 27 2007
EXTENSIONS
a(14)-a(16) from David Radcliffe, Dec 25 2017
a(17) from David Radcliffe, Dec 26 2017
a(18)-a(24) from John Mason, Dec 11 2021
STATUS
approved

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Last modified July 23 16:21 EDT 2024. Contains 374552 sequences. (Running on oeis4.)