A253882 Number of 3-connected planar triangulations of the sphere with n vertices up to orientation preserving isomorphisms.

1, 1, 2, 6, 17, 73, 389, 2274, 14502, 97033, 672781, 4792530, 34911786, 259106122, 1954315346, 14949368524, 115784496932, 906736988527, 7171613842488, 57231089062625, 460428456484557, 3731572377382341, 30447133566946517, 249968326771680542, 2063931874299323140

Offset

4,3

Links

Andrew Howroyd, Table of n, a(n) for n = 4..500

CombOS - Combinatorial Object Server, generate planar graphs

Pascal Honvault, Equivalent classes of degree sequences for triangulated polyhedra and their convex realization, Contributions to Disc. Math. (2021) Vol. 16, No. 1, 128-137.

Pascal Honvault, Local geometry of polyhedra, hal-03744217 [math], 2022.

The House of Graphs, Planar graphs

Prog

(PARI) a(n)={if(n<3, 0, (2*binomial(4*(n-3)+1, n-3)/((n-2)*(3*n-7))
  + 3*sumdiv(n-2, d, if(d>=2, my(s=(n-2)/d); eulerphi(d)*binomial(4*s, s))/4)
  + if(n%2==1, my(s=(n-3)/2); 3*binomial(4*s, s)*(2*s+1)/(3*s+1))
  + if(n%3==1, my(s=(n-4)/3); 8*binomial(4*s, s)*(4*s+1)/(3*s+1))
  + if(n%3==0, my(s=(n-3)/3); 2*binomial(4*s, s)) )/(6*(n-2)))} \\ Andrew Howroyd, Mar 02 2021

Crossrefs

Cf. A000109 (full automorphism group), A000260 (rooted at an edge), A000944, A002709 (with a distinguished face).

Sequence in context: A346043 A079456 A264761 * A327698 A183757 A356011

Adjacent sequences: A253879 A253880 A253881 * A253883 A253884 A253885

Keyword

nonn

Author

Danny Rorabaugh, Feb 27 2015

Extensions

Name clarified and terms a(24) and beyond from Andrew Howroyd, Mar 02 2021

Status

approved