A005500 - OEIS

%I M1516 #40 Feb 23 2021 10:05:55

%S 1,2,5,18,88,489,3071,20667,146381,1072760,8071728,61990477,484182622,

%T 3835654678,30757242535,249255692801,2038827903834,16815060576958,

%U 139706974995635,1168468902294726,9831504782276593,83174244225508659,707159273362126228,6039827641569969225

%N Number of unrooted triangulations of a quadrilateral with n internal nodes.

%C These are also called [n,1]-triangulations.

%C Graphs can be enumerated and counted using the tool "plantri", in particular the command "./plantri -s -P4 -c2m2 [n]". - _Manfred Scheucher_, Mar 08 2018

%D C. F. Earl and L. J. March, Architectural applications of graph theory, pp. 327-355 of R. J. Wilson and L. W. Beineke, editors, Applications of Graph Theory. Academic Press, NY, 1979.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Andrew Howroyd, <a href="/A005500/b005500.txt">Table of n, a(n) for n = 0..200</a>

%H G. Brinkmann and B. McKay, <a href="http://users.cecs.anu.edu.au/~bdm/plantri/">Plantri (program for generation of certain types of planar graph)</a>

%H C. F. Earl and L. J. March, <a href="/A005500/a005500_1.pdf">Architectural applications of graph theory</a>, pp. 327-355 of R. J. Wilson and L. W. Beineke, editors, Applications of Graph Theory. Academic Press, NY, 1979. (Annotated scanned copy)

%H C. F. Earl & N. J. A. Sloane, <a href="/A005500/a005500.pdf">Correspondence, 1980-1981</a>

%F a(n) = (A005505(n) + A002710(n))/2. - _Max Alekseyev_, Oct 29 2012

%Y Column k=1 of A169808.

%Y Cf. A002710, A005505.

%K nonn

%O 0,2

%A _N. J. A. Sloane_

%E Edited by _Max Alekseyev_, Oct 29 2012

%E a(7)-a(12) from _Manfred Scheucher_, Mar 08 2018

%E Name clarified and terms a(13) and beyond from _Andrew Howroyd_, Feb 22 2021