A355839 Number of vertices 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.

5, 25, 133, 357, 1013, 1637, 3761, 5561, 9313, 13065, 21689, 25357, 41553, 50157, 66005, 84897, 117793, 129841, 181717, 198857, 251189, 302293, 383161, 401073, 517193, 587041, 687765, 763425, 949869, 966249, 1234425, 1320913, 1512233, 1703657, 1912765, 2023569, 2475361, 2649813, 2934997

Offset

1,1

Comments

This sequence is similar to A355799 but here the corner vertices of the square are also connected to points on the opposite edge.

Links

Table of n, a(n) for n=1..39.

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 = 5.

Scott R. Shannon, Image for n = 6.

Scott R. Shannon, Image for n = 11.

Formula

a(n) = A355840(n) - A355838(n) + 1 by Euler's formula.

Crossrefs

Cf. A355838 (regions), A355840 (edges), A355841 (k-gons), A355799 (without corner vertices), A290131, A331452, A335678.

Sequence in context: A094602 A207834 A351187 * A344396 A351587 A225963

Adjacent sequences: A355836 A355837 A355838 * A355840 A355841 A355842

Keyword

nonn

Author

Scott R. Shannon, Jul 18 2022

Status

approved