A370978 Draw a regular n-gon and the enclosing circle, then for each pair of vertices X, Y, draw a circle with diameter XY; the union of these figures is the graph H_n; sequence gives number of regions in H_n.

1, 3, 16, 16, 81, 91, 302, 272, 829, 831, 1926, 1752, 3849, 3739, 6916, 6464, 11799, 11143, 18374, 17180, 27679, 26819, 40136, 37200, 56901, 54679, 77788, 74816, 103821, 101071, 136928, 131776, 176683, 172143, 224036, 216936, 281201, 273867, 348700, 337520, 426073, 416683

Offset: 1

Author

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

Keywords

• nonn

Comments

H_n is the union of the graph G_n defined in A370976 and the polygon through the initial n points.

Links

• Scott R. Shannon, Image for n = 3.
• Scott R. Shannon, Image for n = 5.

Crossrefs

Cf. A358746, A358782, A358783, A370976, A370977, A370979.

Formula

a(n) = A358782(n) + n if n even, a(n) = A358782(n) + 3*n if n odd.