A370976 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 regions in G_n.

1, 1, 10, 12, 71, 85, 288, 264, 811, 821, 1904, 1740, 3823, 3725, 6886, 6448, 11765, 11125, 18336, 17160, 27637, 26797, 40090, 37176, 56851, 54653, 77734, 74788, 103763, 101041, 136866, 131744, 176617, 172109, 223966, 216900, 281127, 273829, 348622, 337480, 425991, 416641

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 edges in G_n see A358746 and A370977.

For other images for n even, see A358782 (for even n, A358782 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 = 6.
• Scott R. Shannon, Image for n = 7.
• Scott R. Shannon, Image for n = 8.
• Scott R. Shannon, Image for n = 11.

Crossrefs

Cf. A358746, A358782, A358783, A370977, A370978, A370979.

Formula

a(n) = A358782(n) if n even, a(n) = A358782(n) + n if n odd.