A355840 Number of edges 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.

8, 64, 316, 852, 2252, 3780, 8140, 12280, 20172, 28592, 45988, 55508, 87588, 107652, 141060, 181312, 246844, 278352, 380108, 424096, 530764, 638564, 799148, 854448, 1082244, 1235048, 1442572, 1612088, 1975908, 2051784, 2565956, 2773616, 3164916, 3566256, 3997652, 4271136, 5137452, 5537756

Offset: 1

Author

Scott R. Shannon, Jul 18 2022

Keywords

• nonn

Comments

This sequence is similar to A355800 but here the corner vertices of the square are also connected to points on the opposite edge.

See A355838 for images of the squares.

Crossrefs

Cf. A355838 (regions), A355839 (vertices), A355841 (k-gons), A355800 (without corner vertices), A290131, A331452, A335678.

Formula

a(n) = A355838(n) + A355839(n) - 1 by Euler's formula.