A096330 Number of 3-connected planar graphs on n labeled nodes.

1, 25, 1227, 84672, 7635120, 850626360, 112876089480, 17381709797760, 3046480841900160, 598731545755324800, 130389773403373545600, 31163616486434838067200, 8109213009296586130944000, 2282014010657773764160588800, 690521215428258768326957184000

Offset

4,2

Comments

Recurrence known, see Bodirsky et al.

References

M. Bodirsky, C. Groepl and M. Kang: Generating Labeled Planar Graphs Uniformly At Random; ICALP03 Eindhoven, LNCS 2719, Springer Verlag (2003), 1095 - 1107.

Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, p. 419.

Links

Gheorghe Coserea, Table of n, a(n) for n = 4..104

M. Bodirsky, C. Groepl and M. Kang, Generating Labeled Planar Graphs Uniformly At Random, Theoretical Computer Science, Volume 379, Issue 3, 15 June 2007, pp. 377-386.

Prog

(PARI)
Q(n, k) = { \\ c-nets with n-edges, k-vertices
  if (k < 2+(n+2)\3 || k > 2*n\3, return(0));
  sum(i=2, k, sum(j=k, n, (-1)^((i+j+1-k)%2)*binomial(i+j-k, i)*i*(i-1)/2*
  (binomial(2*n-2*k+2, k-i)*binomial(2*k-2, n-j) -
  4*binomial(2*n-2*k+1, k-i-1)*binomial(2*k-3, n-j-1))));
};
a(n) = sum(k=(3*n+1)\2, 3*n-6, n!*Q(k, n)/(4*k));
apply(a, [4..18]) \\ Gheorghe Coserea, Aug 11 2017

Crossrefs

Cf. A066537, A096331, A096332, A290326.

Sequence in context: A014769 A012851 A181719 * A174751 A042203 A042200

Adjacent sequences: A096327 A096328 A096329 * A096331 A096332 A096333

Keyword

nonn

Author

Steven Finch, Aug 02 2004

Status

approved