cp's OEIS Frontend

A355838 Number of regions formed in a square by straight line segments when connecting the n+1 points along each edge that divide it into n equal parts to the n+1 points on the edge on the opposite side of the square.

%I A355838 #12 Jul 20 2022 10:11:28
%S A355838 4,40,184,496,1240,2144,4380,6720,10860,15528,24300,30152,46036,57496,
%T A355838 75056,96416,129052,148512,198392,225240,279576,336272,415988,453376,
%U A355838 565052,648008,754808,848664,1026040,1085536,1331532,1452704,1652684,1862600,2084888,2247568,2662092,2887944,3193744
%N A355838 Number of regions formed in a square by straight line segments when connecting the n+1 points along each edge that divide it into n equal parts to the n+1 points on the edge on the opposite side of the square.
%C A355838 This sequence is similar to A355798 but here the corner vertices of the square are also connected to points on the opposite edge.
%H A355838 Scott R. Shannon, <a href="/A355838/a355838.jpg">Image for n = 2</a>.
%H A355838 Scott R. Shannon, <a href="/A355838/a355838_1.jpg">Image for n = 3</a>.
%H A355838 Scott R. Shannon, <a href="/A355838/a355838_2.jpg">Image for n = 4</a>.
%H A355838 Scott R. Shannon, <a href="/A355838/a355838_3.jpg">Image for n = 5</a>.
%H A355838 Scott R. Shannon, <a href="/A355838/a355838_4.jpg">Image for n = 6</a>.
%H A355838 Scott R. Shannon, <a href="/A355838/a355838_5.jpg">Image for n = 7</a>.
%H A355838 Scott R. Shannon, <a href="/A355838/a355838_6.jpg">Image for n = 8</a>.
%H A355838 Scott R. Shannon, <a href="/A355838/a355838_7.jpg">Image for n = 11</a>.
%H A355838 Scott R. Shannon, <a href="/A355838/a355838_8.jpg">Image for n = 16</a>.
%F A355838 a(n) = A355840(n) - A355839(n) + 1 by Euler's formula.
%Y A355838 Cf. A355839 (vertices), A355840 (edges), A355841 (k-gons), A355798 (without corner vertices), A290131, A331452, A335678.
%K A355838 nonn
%O A355838 1,1
%A A355838 _Scott R. Shannon_, Jul 18 2022