cp's OEIS Frontend

A357060 Number of vertices in a square when n internal squares are drawn between the 4n points that divide each side into n+1 equal parts.

%I A357060 #23 Sep 17 2022 13:06:58
%S A357060 4,8,20,40,68,88,148,168,260,296,404,436,580,632,788,840,1028,1072,
%T A357060 1300,1384,1604,1688,1940,1972,2308,2408,2708,2808,3140,3220,3604,
%U A357060 3696,4084,4232,4628,4716,5188,5336,5764,5908,6404,6496,7060,7224,7732,7928,8468,8524,9220,9368,9988,10216
%N A357060 Number of vertices in a square when n internal squares are drawn between the 4n points that divide each side into n+1 equal parts.
%C A357060 The even values of n that yield squares with non-simple intersections are 32, 38, 44, 50, 54, 62, 76, 90, 98, ... .
%H A357060 Scott R. Shannon, <a href="/A357060/a357060.png">Image for n = 1</a>.
%H A357060 Scott R. Shannon, <a href="/A357060/a357060_1.png">Image for n = 2</a>.
%H A357060 Scott R. Shannon, <a href="/A357060/a357060_2.png">Image for n = 3</a>.
%H A357060 Scott R. Shannon, <a href="/A357060/a357060_3.png">Image for n = 5</a>. This is the first term that forms squares with non-simple intersections.
%H A357060 Scott R. Shannon, <a href="/A357060/a357060_4.png">Image for n = 10</a>.
%H A357060 Scott R. Shannon, <a href="/A357060/a357060_5.png">Image for n = 32</a>. This is the first term with n mod 2 = 0 that forms squares with non-simple intersections.
%H A357060 Scott R. Shannon, <a href="/A357060/a357060_6.png">Image for n = 200</a>.
%F A357060 a(n) = A357061(n) - A357058(n) + 1 by Euler's formula.
%F A357060 Conjecture: a(n) = 4*n^2 + 4 for squares that only contain simple intersections when cut by n internal squares. This is never the case for odd n >= 5.
%Y A357060 Cf. A357058 (regions), A357061 (edges), A355949, A355839, A355799, A357007 (triangle).
%K A357060 nonn
%O A357060 0,1
%A A357060 _Scott R. Shannon_, Sep 10 2022