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

1,1

Links

Table of n, a(n) for n=1..47.

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

Crossrefs

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

Sequence in context: A062989 A122679 A264132 * A147114 A296669 A131537

Adjacent sequences: A355946 A355947 A355948 * A355950 A355951 A355952

Keyword

nonn

Author

Scott R. Shannon, Jul 21 2022

Status

approved