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Search: id:A124479
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| A124479 |
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From the game of Quod: number of "squares" on an n X n array of points with the four corner points deleted. |
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+0
1
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| 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; listen)
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OFFSET
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2,3
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COMMENT
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We count all squares whose vertices are among the points; the sides of the squares need not be horizontal or vertical.
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REFERENCES
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Ian Stewart, How To Cut A Cake: and Other Mathematical Conundrums, Chap. 7.
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FORMULA
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(n^4 - n^2 - 48*n + 84)/12.
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EXAMPLE
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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.
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CROSSREFS
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Sequence in context: A122728 A031381 A090950 this_sequence A140373 A003020 A075024
Adjacent sequences: A124476 A124477 A124478 this_sequence A124480 A124481 A124482
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KEYWORD
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nonn
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AUTHOR
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Joshua Zucker, Dec 18 2006
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EXTENSIONS
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Additional comments from Dean Hickerson, Dec 18 2006
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