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A253882 Number of 3-connected planar triangulations of the sphere with n vertices up to orientation preserving isomorphisms. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
4,3
LINKS
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
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

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Last modified April 23 06:04 EDT 2024. Contains 371906 sequences. (Running on oeis4.)