A370976 - OEIS

%I #23 Mar 26 2024 07:27:37

%S 1,1,10,12,71,85,288,264,811,821,1904,1740,3823,3725,6886,6448,11765,

%T 11125,18336,17160,27637,26797,40090,37176,56851,54653,77734,74788,

%U 103763,101041,136866,131744,176617,172109,223966,216900,281127,273829,348622,337480,425991,416641

%N 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.

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

%C 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 For the numbers of vertices and edges in G_n see A358746 and A370977.

%C For other images for n even, see A358782 (for even n, A358782 and the present sequence agree).

%H Scott R. Shannon, <a href="/A370976/a370976.jpg">Image for n = 3</a>.

%H Scott R. Shannon, <a href="/A358782/a358782_2.jpg">Image for n = 4</a>.

%H Scott R. Shannon, <a href="/A358782/a358782_4.jpg">Image for n = 6</a>.

%H Scott R. Shannon, <a href="/A370976/a370976_1.jpg">Image for n = 7</a>.

%H Scott R. Shannon, <a href="/A358782/a358782_5.jpg">Image for n = 8</a>.

%H Scott R. Shannon, <a href="/A370976/a370976_2.jpg">Image for n = 11</a>.

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

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

%K nonn

%O 1,3

%A _Scott R. Shannon_ and _N. J. A. Sloane_, Mar 25 2024