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Number of connected simple graphs with n vertices, n+2 edges, and vertex degrees no more than 4.
7

%I #16 Jun 05 2023 09:59:48

%S 0,0,0,1,4,18,79,326,1278,4875,17978,64720,227842,787546,2678207,

%T 8982754,29761361,97558039,316778169,1019996738,3259673935,

%U 10347077497,32644696187,102425388286,319754805262

%N Number of connected simple graphs with n vertices, n+2 edges, and vertex degrees no more than 4.

%H J. B. Hendrickson and C. A. Parks, <a href="https://doi.org/10.1021/ci00001a018">Generation and Enumeration of Carbon skeletons</a>, J. Chem. Inf. Comput. Sci., 31 (1991), 101-107. See Table 2, column 3 on page 103.

%H Michael A. Kappler, <a href="http://www.daylight.com/meetings/emug04/Kappler/GenSmi.html">GENSMI: Exhaustive Enumeration of Simple Graphs</a>. [gives different a(18)]

%o (nauty/bash)

%o for n in {4..15}; do geng -c -D4 ${n} $((n+2)):$((n+2)) -u; done # _Andrey Zabolotskiy_, Nov 24 2017

%Y The analogs for n+k edges with k = -1, 0, ..., 7 are: A000602, A036671, A112410, this sequence, A112408, A112424, A112425, A112426, A112442. Cf. A121941.

%K nonn

%O 1,5

%A _Jonathan Vos Post_, Dec 21 2005

%E Corrected offset and new name from _Andrey Zabolotskiy_, Nov 24 2017

%E a(18) corrected and a(19)-a(25) added by _Georg Grasegger_, Jun 05 2023