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

1,1

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.

Links

Table of n, a(n) for n=1..38.

Formula

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

Crossrefs

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

Sequence in context: A189690 A188741 A188993 * A223681 A189065 A189190

Adjacent sequences: A355837 A355838 A355839 * A355841 A355842 A355843

Keyword

nonn

Author

Scott R. Shannon, Jul 18 2022

Status

approved