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A370977 Let G_n denote the planar graph defined in A358746 with the addition, if n is odd, of the circle containing the initial n points; sequence gives the number of edges in G_n.

%I A370977 #24 Mar 26 2024 23:06:18
%S A370977 1,2,15,16,125,138,539,432,1557,1450,3707,3120,7501,6874,13575,12000,
%T A370977 23273,20970,36347,32400,54873,51194,79695,70752,113125,105274,154791,
%U A370977 144480,206741,195810,272831,255808,352209,335002,446775,422784,560957,534698,695799,659440,850381,815682
%N A370977 Let G_n denote the planar graph defined in A358746 with the addition, if n is odd, of the circle containing the initial n points; sequence gives the number of edges in G_n.
%C A370977 If n is even the circle through the initial n points is already part of the graph.
%C A370977 In other words, draw a circle and place n equally spaced points around it; for each pair of poins X, Y, draw a circle with diameter XY; the union of these circles is the graph G_n.
%C A370977 For the numbers of vertices and regions in G_n see A358746 and A370976.
%C A370977 For other images for n even, see A358746 (for even n, A358783 and the present sequence agree).
%H A370977 Scott R. Shannon, <a href="/A370977/a370977.jpg">Image for n = 3</a>.
%H A370977 Scott R. Shannon, <a href="/A358746/a358746_7.jpg">Image for n = 4</a>.
%H A370977 Scott R. Shannon, <a href="/A370977/a370977_1.jpg">Image for n = 5</a>.
%H A370977 Scott R. Shannon, <a href="/A358746/a358746_9.jpg">Image for n = 6</a>.
%H A370977 Scott R. Shannon, <a href="/A370977/a370977_2.jpg">Image for n = 7</a>.
%H A370977 Scott R. Shannon, <a href="/A358746/a358746_11.jpg">Image for n = 8</a>.
%F A370977 a(n) = A358783(n) if n even, a(n) = A358783(n) + n if n odd.
%Y A370977 Cf. A358746, A358782, A358783, A370976, A370978, A370979.
%K A370977 nonn
%O A370977 1,2
%A A370977 _Scott R. Shannon_ and _N. J. A. Sloane_, Mar 25 2024