A112426 Number of connected simple graphs with n vertices, n+6 edges, and vertex degrees no more than 4.

0, 0, 0, 0, 0, 1, 9, 134, 1714, 18436, 167703, 1327240, 9372119, 60324933, 359730035, 2012733260, 10670975762, 54028108819, 262872075003, 1235323112178, 5630370812614

Offset

1,7

Comments

Distribution of carbon skeletons. See the paper by Hendrikson and Parks for details. If n=6 the number of 7-cyclic skeletons is 1. If n=7 the number of 7-cyclic skeletons is 9. If n=10 the number of 7-cyclic skeletons is 18436. - Parthasarathy Nambi, Jan 05 2007

Links

Table of n, a(n) for n=1..21.

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 7 on page 103.

Michael A. Kappler, GENSMI: Exhaustive Enumeration of Simple Graphs [gives different numbers for n > 10].

Prog

(nauty/bash)
for n in {6..13}; do geng -c -D4 ${n} $((n+6)):$((n+6)) -u; done # Andrey Zabolotskiy, Nov 24 2017

Crossrefs

The analogs for n+k edges with k = -1, 0, ..., 7 are: A000602, A036671, A112410, A112619, A112408, A112424, A112425, this sequence, A112442. Cf. A121941.

Sequence in context: A110273 A082760 A268654 * A213688 A163200 A279975

Adjacent sequences: A112423 A112424 A112425 * A112427 A112428 A112429

Keyword

nonn,more

Author

Jonathan Vos Post, Dec 21 2005

Extensions

New name, offset corrected, and a(11)-a(14) corrected by Andrey Zabolotskiy, Nov 24 2017

a(15)-a(21) added by Georg Grasegger, Jun 05 2023

Status

approved