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.

A384700 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 circles created.

This page as a plain text file.
%I A384700 #16 Jun 15 2025 14:36:30
%S A384700 0,1,9,24,52,93,153,232,336,465,625,816,1044,1309,1617,1968,2368,2817,
%T A384700 3321,3880,4500,5181,5929
%N A384700 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 circles created.
%H A384700 Scott R. Shannon, <a href="/A384700/a384700.jpg">Image for a(3) = 9</a>.
%F A384700 Conjecture:
%F A384700 for even n, a(n) = n^3/2 - n^2/4 - n,
%F A384700 for odd n > 1, a(n) = n^3/2 - n^2/4 - n + 3/4.
%Y A384700 Cf. A384701 (vertices), A384702 (regions), A384703 (edges), A365669, A374338, A373110, A372981,
%K A384700 nonn,more
%O A384700 1,3
%A A384700 _Scott R. Shannon_ and _N. J. A. Sloane_, Jun 07 2025