cp's OEIS Frontend

A112410 Number of connected simple graphs with n vertices, n+1 edges, and vertex degrees no more than 4.

%I A112410 #21 Jun 02 2025 16:32:07
%S A112410 0,0,0,1,5,17,56,182,573,1792,5533,16977,51652,156291,470069,1407264,
%T A112410 4193977,12451760,36838994,108656009,319583578,937634011,2744720126,
%U A112410 8018165821,23379886511,68056985580,197800670948,574068309840,1663907364480,4816910618093,13929036720057
%N A112410 Number of connected simple graphs with n vertices, n+1 edges, and vertex degrees no more than 4.
%C A112410 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
%C A112410 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
%H A112410 Andrew Howroyd, <a href="/A112410/b112410.txt">Table of n, a(n) for n = 1..200</a>
%H A112410 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 2 on page 103.
%H A112410 Michael A. Kappler, <a href="http://www.daylight.com/meetings/emug04/Kappler/GenSmi.html">GENSMI: Exhaustive Enumeration of Simple Graphs</a>.
%F A112410 a(n) = A125669(n) + A125670(n) + A125671(n) + A305132(n). - _Andrew Howroyd_, May 26 2018
%e A112410 The only such graph for n = 4 is:
%e A112410 o-o
%e A112410 |/|
%e A112410 o-o
%o A112410 (nauty)
%o A112410 for n in {4..15}; do geng -c -D4 ${n} $((n+1)):$((n+1)) -u; done # _Andrey Zabolotskiy_, Nov 24 2017
%Y A112410 The analogs for n+k edges with k = -1, 0, ..., 7 are: A000602, A036671, this sequence, A112619, A112408, A112424, A112425, A112426, A112442.
%Y A112410 Cf. A121941 (any number of edges), A006820 (2n edges).
%Y A112410 Cf. A125669, A125670, A125671, A305132.
%K A112410 nonn
%O A112410 1,5
%A A112410 _Jonathan Vos Post_, Dec 08 2005
%E A112410 Corrected offset and new name from _Andrey Zabolotskiy_, Nov 20 2017
%E A112410 a(20) corrected by _Andrey Zabolotskiy_ and _Andrew Howroyd_, May 26 2018
%E A112410 Terms a(21) and beyond from _Andrew Howroyd_, May 26 2018