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A112410
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Number of connected simple graphs with n vertices, n+1 edges, and vertex degrees no more than 4.
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9
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0, 0, 0, 1, 5, 17, 56, 182, 573, 1792, 5533, 16977, 51652, 156291, 470069, 1407264, 4193977, 12451760, 36838994, 108656009, 319583578, 937634011, 2744720126, 8018165821, 23379886511, 68056985580, 197800670948, 574068309840, 1663907364480, 4816910618093, 13929036720057
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OFFSET
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1,5
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COMMENTS
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Such graphs are also referred to (e.g., by Hendrickson & Parks) as carbon skeletons with two rings, or bicyclic skeletons, although actual number of simple cycles in such graphs can exceed 2 (e.g., in the example). - Andrey Zabolotskiy, Nov 24 2017
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LINKS
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FORMULA
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EXAMPLE
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The only such graph for n = 4 is:
o-o
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o-o
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PROG
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(nauty/bash)
for n in {4..15}; do geng -c -D4 ${n} $((n+1)):$((n+1)) -u; done # Andrey Zabolotskiy, Nov 24 2017
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CROSSREFS
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The analogs for n+k edges with k = -1, 0, ..., 7 are: A000602, A036671, this sequence, A112619, A112408, A112424, A112425, A112426, A112442.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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