OFFSET
1,1
COMMENTS
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.
LINKS
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.
EXAMPLE
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:
*---*
| |
*---* *---*
| |
*---* *---*
| |
*---*
.
For n = 3 the board contains 20 vertices, represented by '*', shown below:
*---*
| |
*---* *---*
| |
*---* *---*
| |
*---* *---*
| |
*---* *---*
| |
*---*
.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Scott R. Shannon and N. J. A. Sloane, Mar 21 2020
EXTENSIONS
a(8)-a(27) from Lars Blomberg, Jun 03 2020
STATUS
approved