|
| |
|
|
A124479
|
|
From the game of Quod: number of "squares" on an n X n array of points with the four corner points deleted.
|
|
0
| |
|
|
0, 1, 11, 37, 88, 175, 311, 511, 792, 1173, 1675, 2321, 3136, 4147, 5383, 6875, 8656, 10761, 13227, 16093, 19400, 23191, 27511, 32407, 37928, 44125, 51051, 58761, 67312, 76763, 87175, 98611, 111136, 124817, 139723, 155925, 173496, 192511, 213047, 235183, 259000
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 2,3
|
|
|
COMMENTS
| We count all squares whose vertices are among the points; the sides of the squares need not be horizontal or vertical.
|
|
|
REFERENCES
| Ian Stewart, How To Cut A Cake: and Other Mathematical Conundrums, Chap. 7.
|
|
|
FORMULA
| (n^4 - n^2 - 48*n + 84)/12.
|
|
|
EXAMPLE
| So for n=3 we have 5 points:
.....O
....OOO
.....O
The only square is formed by the 4 outer points, agreeing with a(3)=1.
For n=4 we have 12 points:
.....OO
....OOOO
....OOOO
.....OO
There are 5 unit squares, 4 tilted ones with sides sqrt(2) and 2 tilted ones with sides sqrt(5), agreeing with a(4)=11.
|
|
|
CROSSREFS
| Sequence in context: A188135 A188382 A090950 * A140373 A003020 A075024
Adjacent sequences: A124476 A124477 A124478 * A124480 A124481 A124482
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Joshua Zucker, Dec 18 2006
|
|
|
EXTENSIONS
| Additional comments from Dean Hickerson, Dec 18 2006
|
| |
|
|
