cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A384701 On a 2 X n grid of vertices, draw a circle through every unordered triple of non-collinear vertices: a(n) is the number of distinct points where circles intersect.

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%I A384701 #19 Jun 15 2025 14:37:11
%S A384701 2,4,18,172,978,3672,11034,27241,60804,122741,232138,412263,697058
%N A384701 On a 2 X n grid of vertices, draw a circle through every unordered triple of non-collinear vertices: a(n) is the number of distinct points where circles intersect.
%H A384701 Scott R. Shannon, <a href="/A384701/a384701.jpg">Image for a(2) = 4</a>.
%H A384701 Scott R. Shannon, <a href="/A384701/a384701_1.jpg">Image for a(3) = 18</a>.
%H A384701 Scott R. Shannon, <a href="/A384701/a384701_2.jpg">Image for a(4) = 172</a>.
%H A384701 Scott R. Shannon, <a href="/A384701/a384701_3.jpg">Image for a(5) = 978</a>.
%F A384701 a(n) = A384703(n) - A384702(n) + 1 by Euler's formula, for n > 1.
%Y A384701 Cf. A384700 (circles), A384702 (regions), A384703 (edges), A359569, A374825, A374338, A373106.
%K A384701 nonn,more
%O A384701 1,1
%A A384701 _Scott R. Shannon_ and _N. J. A. Sloane_, Jun 07 2025