A007100 Number of labeled trivalent (or cubic) 3-connected graphs with 2n nodes.

1, 70, 16800, 9238320, 9520156800, 16305064776000, 42856575521760000, 163329351308323200000, 864876880105205071104000, 6155146233167046820024320000, 57316399761348433188962519040000

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn

References

• R. W. Robinson, personal communication.
• R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• R. W. Robinson, Table of n, a(n) for n = 2..28
• R. W. Robinson, Cubic labeled graphs, computer print-out, n.d. (see last page)

Formula

a(n) = (2*n)!*r(n)/(3*n*2^n) where r(2) = 1 and r(n) = (3*n-2) * (r(n-1) + Sum_{i=2..n-2} r(i) * r(n-i)). - Sean A. Irvine, Oct 11 2017