cp's OEIS Frontend

A374337 Start with two vertices and draw a circle around each whose radius is the distance between the vertices. The sequence gives the number of regions constructed after n iterations of drawing circles with this same radius around every new vertex created from all circles' intersections.

%I A374337 #17 Jul 06 2024 09:23:00
%S A374337 3,11,27,55,99,145,203,277,353,441,545,651,769,903,1039,1187,1351,
%T A374337 1517,1695,1889,2085,2293,2517,2743,2981,3235,3491,3759,4043,4329,
%U A374337 4627,4941,5257,5585,5929,6275,6633,7007,7383,7771,8175,8581,8999,9433,9869,10317,10781,11247,11725,12219,12715
%N A374337 Start with two vertices and draw a circle around each whose radius is the distance between the vertices. The sequence gives the number of regions constructed after n iterations of drawing circles with this same radius around every new vertex created from all circles' intersections.
%C A374337 See A374338 for further details.
%H A374337 Scott R. Shannon, <a href="/A374337/a374337.jpg">Image for n = 1</a>. In this and other images the initial vertices that form the circles' centers are shown as white dots.
%H A374337 Scott R. Shannon, <a href="/A374337/a374337_1.jpg">Image for n = 2</a>.
%H A374337 Scott R. Shannon, <a href="/A374337/a374337_2.jpg">Image for n = 3</a>.
%H A374337 Scott R. Shannon, <a href="/A374337/a374337_3.jpg">Image for n = 4</a>.
%H A374337 Scott R. Shannon, <a href="/A374337/a374337_4.jpg">Image for n = 16</a>.
%F A374337 a(n) = A374339(n) - A374338(n) + 1, by Euler's formula.
%F A374337 Conjectured:
%F A374337 If n = 3*k + 1, k >= 0, a(n) = |(15*n^2 - 17*n - 7)/3|.
%F A374337 If n = 3*k, k >= 1, a(n) = (15*n^2 - 17*n - 3)/3.
%F A374337 If n = 3*k - 1, k >= 1, a(n) = (15*n^2 - 17*n + 7)/3.
%Y A374337 Cf. A374338 (vertices), A374339 (edges), A359570, A371374, A371253.
%K A374337 nonn
%O A374337 1,1
%A A374337 _Scott R. Shannon_, Jul 05 2024