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A333434
The number of regions inside a diagonal-edged (or diamond-shaped) checkerboard of width and height 2*n-1 formed by the straight line segments mutually connecting any two of the 8*n-4 vertices on the perimeter.
4
4, 104, 1080, 5220, 15508, 39088, 81464, 144292, 261544, 415552, 610460, 942032, 1303848, 1803360, 2461232, 3250284, 4182552, 5269080, 6818764, 8326188, 10336548, 12621292, 14882600, 18368708, 21377496, 25168908, 29994204
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.
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
Cf. A333458 (n-gons), A333459 (vertices), A333460 (edges), A331452, A331456, A331911.
Sequence in context: A211150 A281534 A006415 * A181396 A354063 A196979
KEYWORD
nonn,more
AUTHOR
EXTENSIONS
a(8)-a(27) from Lars Blomberg, Jun 03 2020
STATUS
approved