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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 Table of n, a(n) for n=1..18. 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 Adjacent sequences: A348092 A348093 A348094 * A348096 A348097 A348098 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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