A355949 Number of vertices formed in a square by straight line segments when connecting the four corner vertices to the points dividing the sides into n equal parts.

5, 25, 81, 157, 301, 381, 665, 821, 1109, 1353, 1825, 1861, 2621, 2881, 3285, 3813, 4645, 4773, 5873, 5953, 6821, 7665, 8761, 8613, 10165, 10921, 11777, 12337, 14173, 13717, 16265, 16581, 17861, 19161, 20093, 20461, 23405, 24145, 25305, 25701, 28885, 28433, 31841, 32077, 33269, 35841, 38185

Offset: 1

Author

Scott R. Shannon, Jul 21 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 = 5.
• Scott R. Shannon, Image for n = 6.
• Scott R. Shannon, Image for n = 11.

Crossrefs

Cf. A108914 (regions), A355948 (edges), A355992 (k-gons), A355839, A331452, A335678.

Formula

a(n) = A355948(n) - A108914(n) + 1 by Euler's formula.