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%I #10 Feb 28 2021 16:35:08
%S 1,2,8,38,219,1404,9714,70454,527235,4037671,31477887,249026400,
%T 1994599707,16147744792,131959532817,1087376999834,9027039627035,
%U 75441790558926,634311771606750,5362639252793358,45565021714371644,388937603694422120,3333984869758146814
%N Number of n-hedra with 2n-5 vertices or 3n-7 edges (the vertices of these are all of degree 3, except one which is of degree 4). Alternatively, the number of polyhedra with n vertices whose faces are all triangular, except one which is tetragonal.
%H Andrew Howroyd, <a href="/A058786/b058786.txt">Table of n, a(n) for n = 5..500</a>
%H CombOS - Combinatorial Object Server, <a href="http://combos.org/plantri">generate planar graphs</a>
%H G. P. Michon, <a href="http://www.numericana.com/data/polyhedra.htm">Counting Polyhedra</a>
%e a(5)=1 because the square pyramid is the only pentahedron with 5=2*5-5 vertices (or 8=3*5-7 edges). Alternatively, a(5)=1 because the square pyramid is the only polyhedron with 5 vertices whose faces are all triangles with only one tetragonal exception.
%o (PARI) A342053ColSeq(25,4) \\ See links in A342053. - _Andrew Howroyd_, Feb 28 2021
%Y Column k=4 of A342053.
%Y Cf. A000109, A002856, A000944, A002840, A058787, A058788, A049337.
%K nonn,nice
%O 5,2
%A _Gerard P. Michon_, Nov 29 2000
%E Terms a(19) and beyond from _Andrew Howroyd_, Feb 27 2021
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