Search: id:A124479
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%I A124479
%S A124479 0,1,11,37,88,175,311,511,792,1173,1675,2321,3136,4147,5383,6875,8656,
               10761,
%T A124479 13227,16093,19400,23191,27511,32407,37928,44125,51051,58761,67312,76763,
%U A124479 87175,98611,111136,124817,139723,155925,173496,192511,213047,235183,259000
%N A124479 From the game of Quod: number of "squares" on an n X n array of points 
               with the four corner points deleted.
%C A124479 We count all squares whose vertices are among the points; the sides of 
               the squares need not be horizontal or vertical.
%D A124479 Ian Stewart, How To Cut A Cake: and Other Mathematical Conundrums, Chap. 
               7.
%F A124479 (n^4 - n^2 - 48*n + 84)/12.
%e A124479 So for n=3 we have 5 points:
%e A124479 .....O
%e A124479 ....OOO
%e A124479 .....O
%e A124479 The only square is formed by the 4 outer points, agreeing with a(3)=1.
%e A124479 For n=4 we have 12 points:
%e A124479 .....OO
%e A124479 ....OOOO
%e A124479 ....OOOO
%e A124479 .....OO
%e A124479 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.
%Y A124479 Sequence in context: A031381 A160023 A090950 this_sequence A140373 A003020 
               A075024
%Y A124479 Adjacent sequences: A124476 A124477 A124478 this_sequence A124480 A124481 
               A124482
%K A124479 nonn
%O A124479 2,3
%A A124479 Joshua Zucker, Dec 18 2006
%E A124479 Additional comments from Dean Hickerson, Dec 18 2006

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