A112619 Number of connected simple graphs with n vertices, n+2 edges, and vertex degrees no more than 4.

0, 0, 0, 1, 4, 18, 79, 326, 1278, 4875, 17978, 64720, 227842, 787546, 2678207, 8982754, 29761361, 97558039, 316778169, 1019996738, 3259673935, 10347077497, 32644696187, 102425388286, 319754805262

Offset: 1

Author

Jonathan Vos Post, Dec 21 2005

Keywords

• nonn

Links

• 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 3 on page 103.
• Michael A. Kappler, GENSMI: Exhaustive Enumeration of Simple Graphs. [gives different a(18)]

Crossrefs

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

Programs

nauty

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

Extensions

Corrected offset and new name from Andrey Zabolotskiy, Nov 24 2017

a(18) corrected and a(19)-a(25) added by Georg Grasegger, Jun 05 2023