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A348095 Number of free n-polysticks embedded in the square lattice with at least one cycle. 3
0, 0, 0, 1, 1, 10, 42, 254, 1331, 7358, 39543, 212911, 1135876, 6039878, 31975124, 168790048, 888664299, 4669177072 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,6
COMMENTS
The number of holes h = e - v + 1 (e = the number of edges and v the number of vertices). - John Mason, Feb 12 2023
LINKS
John Mason, Examples of size 6
FORMULA
a(n) + A056841(n+1) = A019988(n).
EXAMPLE
The 4-stick with a cycle is the unit square. The 5-stick with a cycle is the unit square with one protruding edge. The 10 6-sticks with a cycle are the unit square with two protruding edges (in various cis, meta, trans configurations) or with a protruding 2-stick at various angles, or a 2x1 rectangle.
Size 6 examples 1 through 5:
+-+ +-+ + + +-+-+
| | | | | | | |
+-+-+-+ +-+-+-+ +-+-+ +-+-+ +-+-+
| | | |
+-+ +-+
Examples 6 through 10:
+ +-+ + + +-+-+ +-+-+
| | | | | | | | |
+-+ +-+-+ +-+-+ +-+-+ +-+-+
| | | |
+-+-+ +-+
CROSSREFS
Cf. A056841 (tree-like), A019988 (free polysticks).
Sequence in context: A087120 A222358 A321314 * A027149 A324512 A077541
KEYWORD
nonn,more
AUTHOR
R. J. Mathar, Sep 30 2021
EXTENSIONS
a(14)-a(18) from John Mason, Jun 01 2023
STATUS
approved

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Last modified June 14 11:26 EDT 2024. Contains 373397 sequences. (Running on oeis4.)