A335350 - OEIS

%I #12 Jun 04 2020 08:07:57

%S 4,25,37,81,109,169,205,289,341,441,485,625,701,825,913,1089,1189,

%T 1369,1461,1661,1805,2025,2141,2389,2549,2809,2929,3249,3405,3721,

%U 3901,4205,4421,4753,4913,5329,5549,5913,6105,6561,6781,7225,7453,7885,8189,8649

%N a(n) is the number of regions formed in a square by dividing each of its sides into n equal parts giving a total of 4*n nodes and drawing straight line segments from node k to node (k+n+1) mod 4*n, 0 <= k < 4*n.

%C For n>1, a(n)-1 is divisible by 4.

%H Lars Blomberg, <a href="/A335350/b335350.txt">Table of n, a(n) for n = 1..500</a>

%H Lars Blomberg, <a href="/A335350/a335350.png">Illustration for n=3</a>

%H Lars Blomberg, <a href="/A335350/a335350_1.png">Illustration for n=4</a>

%H Lars Blomberg, <a href="/A335350/a335350_2.png">Illustration for n=5</a>

%H Lars Blomberg, <a href="/A335350/a335350_3.png">Illustration for n=10</a>

%H Lars Blomberg, <a href="/A335350/a335350_4.png">Illustration for n=16</a>

%H Lars Blomberg, <a href="/A335350/a335350_5.png">Illustration for n=35</a>

%Y Cf. A335351 (edges), A335352 (vertices), A335353 (n-gons), A335354 (edges in central polygon), A255011, A335057, A335192.

%K nonn

%O 1,1

%A _Lars Blomberg_, Jun 03 2020