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%I #22 Dec 24 2022 11:05:24
%S 2,13,46,101,226,417,744,1169,1802,2599,3742,5139,7022,9261,12110,
%T 15367,19456,24117,29858,36323,43950,52595,62784,73931,86806,101059,
%U 117364,135155,155506
%N Number of vertices among all distinct circles that can be constructed from n equally spaced points along a line using only a compass.
%C A circle is constructed for every pair of the n points, the first point defines the circle's center while the second the radius distance. The number of distinct circles constructed for n points is A001859(n-1).
%C No formula for a(n) is currently known.
%H Scott R. Shannon, <a href="/A359252/a359252.jpg">Image for n = 2</a>.
%H Scott R. Shannon, <a href="/A359252/a359252_1.jpg">Image for n = 3</a>.
%H Scott R. Shannon, <a href="/A359252/a359252_2.jpg">Image for n = 4</a>.
%H Scott R. Shannon, <a href="/A359252/a359252_3.jpg">Image for n = 5</a>.
%H Scott R. Shannon, <a href="/A359252/a359252_4.jpg">Image for n = 6</a>.
%H Scott R. Shannon, <a href="/A359252/a359252_5.jpg">Image for n = 10</a>.
%H Scott R. Shannon, <a href="/A359252/a359252_7.jpg">Image for n = 11</a>.
%H Scott R. Shannon, <a href="/A359252/a359252_6.jpg">Image for n = 20</a>.
%F a(n) = A359254(n) - A359253(n) + 1 by Euler's formula.
%Y Cf. A359253 (regions), A359254 (edges), A359258 (k-gons), A001859, A290447, A331702, A358746.
%K nonn,more
%O 2,1
%A _Scott R. Shannon_, Dec 22 2022