%I #23 Jun 05 2023 08:31:04

%S 0,0,0,0,0,1,9,134,1714,18436,167703,1327240,9372119,60324933,

%T 359730035,2012733260,10670975762,54028108819,262872075003,

%U 1235323112178,5630370812614

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

%C 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

%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 7 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 numbers for n > 10].

%o (nauty/bash)

%o for n in {6..13}; do geng -c -D4 ${n} $((n+6)):$((n+6)) -u; done # _Andrey Zabolotskiy_, Nov 24 2017

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

%K nonn,more

%O 1,7

%A _Jonathan Vos Post_, Dec 21 2005

%E New name, offset corrected, and a(11)-a(14) corrected by _Andrey Zabolotskiy_, Nov 24 2017

%E a(15)-a(21) added by _Georg Grasegger_, Jun 05 2023