cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A279022 Greatest possible number of diagonals of a polyhedron having n edges.

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%I A279022 #10 Dec 03 2016 13:07:13
%S A279022 0,1,1,2,4,5,7,10,13,16,20,23,28,34,37,44,52,55,64,73,77,88,100,103,
%T A279022 115,128,133
%N A279022 Greatest possible number of diagonals of a polyhedron having n edges.
%C A279022 Note that a polyhedron with 6 edges (a tetrahedron) has no diagonals and a polyhedron having exactly 7 edges does not exist.
%C A279022 If n = 3k where k > 3 than the maximum number of diagonals is achieved by a simple polyhedron with k+2 faces.
%C A279022 According to the Grünbaum-Motzkin Theorem a(3k) = 2*k^2-13*k+30, for all k>11.
%C A279022 Additionally for all k>11 a(3k+1) <= 2*k^2-13*k+36 and a(3k+2) <= 2*k^2-11*k+27.
%D A279022 1. B. Grünbaum, Convex Polytopes, 2nd edition, Springer, 2003.
%H A279022 B. Grünbaum, T. S. Motzkin, <a href="http://cms.math.ca/10.4153/CJM-1963-071-3">The number of hexagons and the simplicity of geodesics of certain polyhedra </a>, Canadian journal of Mathematics, 15 (1963), pp. 744-751.
%Y A279022 Cf. A002840, A279015, A279019.
%K A279022 nonn,more
%O A279022 8,4
%A A279022 _Vladimir Letsko_, Dec 03 2016