1,1

The diagonal-edged checker board of width and height 2*n-1 contains 8*n-4 vertices lying on a 2D square grid as shown in the examples below. Join every pair of vertices by a line segment, provided the line does not extend beyond the boundary of the board. The sequence gives the number of regions in the resulting figure.

Scott R. Shannon, Illustration for n = 2.

Scott R. Shannon, Illustration for n = 3.

Scott R. Shannon, Illustration for n = 4.

Scott R. Shannon, Illustration for n = 5.

Scott R. Shannon, Illustration for n = 6.

Scott R. Shannon, Illustration for n = 2 using random distance-based coloring.

Scott R. Shannon, Illustration for n = 3 using random distance-based coloring.

Scott R. Shannon, Illustration for n = 4 using random distance-based coloring.

Scott R. Shannon, Illustration for n = 5 using random distance-based coloring.

Scott R. Shannon, Illustration for n = 6 using random distance-based coloring.

For n = 1 the board is a single square with 4 vertices on the corners.

For n = 2 the board contains 12 vertices, represented by '*', shown below:

*---*

| |

*---* *---*

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*---* *---*

| |

*---*

.

For n = 3 the board contains 20 vertices, represented by '*', shown below:

*---*

| |

*---* *---*

| |

*---* *---*

| |

*---* *---*

| |

*---* *---*

| |

*---*

.

Cf. A333458 (n-gons), A333459 (vertices), A333460 (edges), A331452, A331456, A331911.

Sequence in context: A211150 A281534 A006415 * A181396 A354063 A196979

Adjacent sequences: A333431 A333432 A333433 * A333435 A333436 A333437

nonn,more

Scott R. Shannon and N. J. A. Sloane, Mar 21 2020

a(8)-a(27) from Lars Blomberg, Jun 03 2020

approved