cp's OEIS Frontend

A358407 Number of regions formed in a square by straight line segments when connecting the n-1 points between each corner that divide each edge into n equal parts to the n-1 points on each of the two adjacent edges of the square.

%I A358407 #15 Nov 16 2022 08:53:43
%S A358407 1,5,37,173,553,1365,2909,5513,9577,15485,24157,35021,51201,71013,
%T A358407 95621,126277,167213,211737,272025,335681,413677,505445,618557,729485,
%U A358407 878017,1034697,1215185,1409273,1654785,1875265,2192281,2486797,2836317,3216833,3633709,4034313,4599789,5124841
%N A358407 Number of regions formed in a square by straight line segments when connecting the n-1 points between each corner that divide each edge into n equal parts to the n-1 points on each of the two adjacent edges of the square.
%H A358407 Scott R. Shannon, <a href="/A358407/a358407.jpg">Image for n = 2</a>.
%H A358407 Scott R. Shannon, <a href="/A358407/a358407_1.jpg">Image for n = 3</a>.
%H A358407 Scott R. Shannon, <a href="/A358407/a358407_2.jpg">Image for n = 4</a>.
%H A358407 Scott R. Shannon, <a href="/A358407/a358407_3.jpg">Image for n = 10</a>.
%H A358407 Scott R. Shannon, <a href="/A358407/a358407_4.jpg">Image for n = 20</a>.
%F A358407 a(n) = A358409(n) - A358408(n) + 1 by Euler's formula.
%Y A358407 Cf. A358408 (vertices), A358409 (edges), A355798, A255011.
%K A358407 nonn
%O A358407 1,2
%A A358407 _Scott R. Shannon_, Nov 14 2022