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.
%I A279019 #86 Oct 27 2024 09:25:28
%S A279019 0,0,2,6,12,20,30,42,56,72,90,110,132,156,182,210,240,272,306,342,380,
%T A279019 420,462,506,552,600,650,702,756,812,870,930,992,1056,1122,1190,1260,
%U A279019 1332,1406,1482,1560,1640,1722,1806,1892,1980,2070,2162,2256,2352,2450
%N A279019 Least possible number of diagonals of simple convex polyhedron with n faces.
%C A279019 Obviously, a pyramid has no diagonals. Hence minimum of diagonals of an arbitrary convex polyhedron having n faces is equal to 0.
%C A279019 Minimum number of diagonals among simple convex polyhedra having n faces is obtained from a polyhedron with two triangular faces, n-4 quadrangular faces and two (n-1)-sided faces. A polyhedron having 3 triangular faces, 3 pentagonal faces and 1 hexagonal face gives another example of a simple convex polyhedron with the least possible number of diagonals for n = 7. A polyhedron having 4 triangular faces and 4 hexagonal faces gives a similar example for n = 8.
%C A279019 Essentially the same as A103505 and A002378. - _R. J. Mathar_, Dec 05 2016
%H A279019 Colin Barker, <a href="/A279019/b279019.txt">Table of n, a(n) for n = 4..1000</a>
%H A279019 David Bremner and Victor Klee, <a href="http://dx.doi.org/10.1006/jcta.1998.2953">Inner Diagonals of Convex Polytopes</a>, Journal of Combinatorial Theory, Series A, Volume 87, Issue 1, July 1999, Pages 175-197.
%H A279019 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A279019 a(n) = n^2 - 9*n + 20 = (n-4)*(n-5).
%F A279019 G.f.: -2*x^6/(x-1)^3. - _R. J. Mathar_, Dec 05 2016
%F A279019 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6. - _Colin Barker_, Dec 05 2016
%F A279019 E.g.f.: exp(x)*(20 - 8*x + x^2) - x^3/3 - 3*x^2 - 12*x - 20. - _Stefano Spezia_, Nov 24 2019
%F A279019 From _Amiram Eldar_, Jul 09 2023: (Start)
%F A279019 Sum_{n>=6} 1/a(n) = 1.
%F A279019 Sum_{n>=6} (-1)^n/a(n) = 2*log(2) - 1. (End)
%t A279019 Table[(n-4)(n-5),{n,4,60}] (* or *) LinearRecurrence[{3,-3,1},{0,0,2},60] (* _Harvey P. Dale_, Sep 23 2019 *)
%o A279019 (PARI) concat(vector(2), Vec(2*x^6 / (1 - x)^3 + O(x^60))) \\ _Colin Barker_, Dec 05 2016
%Y A279019 Cf. A000944, A002378, A279015, A279022, A007531.
%K A279019 nonn,easy
%O A279019 4,3
%A A279019 _Vladimir Letsko_, Dec 03 2016