A335350 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.

4, 25, 37, 81, 109, 169, 205, 289, 341, 441, 485, 625, 701, 825, 913, 1089, 1189, 1369, 1461, 1661, 1805, 2025, 2141, 2389, 2549, 2809, 2929, 3249, 3405, 3721, 3901, 4205, 4421, 4753, 4913, 5329, 5549, 5913, 6105, 6561, 6781, 7225, 7453, 7885, 8189, 8649

Offset: 1

Author

Lars Blomberg, Jun 03 2020

Keywords

• nonn

Comments

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

Links

• Lars Blomberg, Table of n, a(n) for n = 1..500
• Lars Blomberg, Illustration for n=3
• Lars Blomberg, Illustration for n=4
• Lars Blomberg, Illustration for n=5
• Lars Blomberg, Illustration for n=10
• Lars Blomberg, Illustration for n=16
• Lars Blomberg, Illustration for n=35

Crossrefs

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