A358408 Number of vertices 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.

4, 8, 32, 144, 468, 1160, 2512, 4836, 8468, 13760, 21784, 31168, 46596, 64760, 86912, 114656, 154400, 194116, 253160, 310408, 382712, 469296, 580688, 677656, 822928, 969880, 1141112, 1319984, 1566512, 1755032, 2080376, 2349188, 2686452, 3052184, 3450348, 3800756, 4387404, 4880560, 5443192

Offset: 1

Author

Scott R. Shannon, Nov 14 2022

Keywords

• nonn

Links

• Scott R. Shannon, Image for n = 2.
• Scott R. Shannon, Image for n = 3.
• Scott R. Shannon, Image for n = 4.
• Scott R. Shannon, Image for n = 10.

Crossrefs

Cf. A358407 (regions), A358409 (edges), A355799, A331449.

Formula

a(n) = A358409(n) - A358407(n) + 1 by Euler's formula.