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 A112410 Number of connected simple graphs with n vertices, n+1 edges, and vertex degrees no more than 4. 9
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS 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 Terms computed with nauty agree at least to a(20) with those computed by formula and sequences A125669, A125670, A125671, A305132. - Andrew Howroyd, May 26 2018 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..200 J. B. Hendrickson and C. A. Parks, Generation and Enumeration of Carbon skeletons, J. Chem. Inf. Comput. Sci., 31 (1991), 101-107. See Table 2, column 2 on page 103. Michael A. Kappler, GENSMI: Exhaustive Enumeration of Simple Graphs. FORMULA a(n) = A125669(n) + A125670(n) + A125671(n) + A305132(n). - Andrew Howroyd, May 26 2018 EXAMPLE The only such graph for n = 4 is: o-o |/| o-o PROG (nauty/bash) for n in {4..15}; do geng -c -D4 \${n} \$((n+1)):\$((n+1)) -u; done # Andrey Zabolotskiy, Nov 24 2017 CROSSREFS The analogs for n+k edges with k = -1, 0, ..., 7 are: A000602, A036671, this sequence, A112619, A112408, A112424, A112425, A112426, A112442. Cf. A121941 (any number of edges), A006820 (2n edges). Cf. A125669, A125670, A125671, A305132. Sequence in context: A081495 A191645 A146240 * A146271 A145371 A112044 Adjacent sequences:  A112407 A112408 A112409 * A112411 A112412 A112413 KEYWORD nonn AUTHOR Jonathan Vos Post, Dec 08 2005 EXTENSIONS Corrected offset and new name from Andrey Zabolotskiy, Nov 20 2017 a(20) corrected by Andrey Zabolotskiy and Andrew Howroyd, May 26 2018 Terms a(21) and beyond from Andrew Howroyd, May 26 2018 STATUS approved

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Last modified May 6 00:41 EDT 2021. Contains 343579 sequences. (Running on oeis4.)