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.

1, 2, 15, 16, 125, 138, 539, 432, 1557, 1450, 3707, 3120, 7501, 6874, 13575, 12000, 23273, 20970, 36347, 32400, 54873, 51194, 79695, 70752, 113125, 105274, 154791, 144480, 206741, 195810, 272831, 255808, 352209, 335002, 446775, 422784, 560957, 534698, 695799, 659440, 850381, 815682

Offset: 1

Author

Scott R. Shannon and N. J. A. Sloane, Mar 25 2024

Keywords

• nonn

Comments

If n is even the circle through the initial n points is already part of the graph.

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.

For the numbers of vertices and regions in G_n see A358746 and A370976.

For other images for n even, see A358746 (for even n, A358783 and the present sequence agree).

Links

• Scott R. Shannon, Image for n = 3.
• Scott R. Shannon, Image for n = 4.
• Scott R. Shannon, Image for n = 5.
• Scott R. Shannon, Image for n = 6.
• Scott R. Shannon, Image for n = 7.
• Scott R. Shannon, Image for n = 8.

Crossrefs

Cf. A358746, A358782, A358783, A370976, A370978, A370979.

Formula

a(n) = A358783(n) if n even, a(n) = A358783(n) + n if n odd.