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A124623 Number of unit squares having center within inscribed circle of an n X n integer square. 1

%I

%S 1,4,9,12,21,32,37,52,69,80,97,112,137,156,177,208,225,256,293,316,

%T 349,384,421,448,489,540,577,616,665,716,749,812,861,912,973,1020,

%U 1085,1124,1201,1264,1313,1396,1457,1528,1597,1664,1741,1804,1885,1976,2053,2128

%N Number of unit squares having center within inscribed circle of an n X n integer square.

%C From _Robert G. Wilson v_, Mar 22 2017: (Start)

%C For n odd, the center of the circle is in the middle of the center square and thus a(2n-1) == 1 (mod 4).

%C For n even, the center of the circle is at the four corners of the center 4 squares and thus a(2n) == 0 (mod 4).

%C a(n) ~ n*Pi/4. (End)

%H Robert G. Wilson v, <a href="/A124623/b124623.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = n^2 - 4*k(n); k(n) = number of exterior centers per quadrant.

%F a(2n-1) = A036704(n-1). - _Robert G. Wilson v_, Mar 28 2017

%F a(2n) = 4*A120883(n-1). - _Robert G. Wilson v_, Mar 28 2017

%t f[n_] := 4*Length[ Select[ Flatten[ Table[ If[ OddQ@ n, x^2 + y^2, x(x -1) + y(y -1) + 1/2], {x, n/2}, {y, n/2}]], 4# < n^2 &]] + If[ OddQ@ n, 2(n -1) + 1, 0]; Array[f, 52] (* _Robert G. Wilson v_, Mar 22 2017 *)

%Y Cf. A051233.

%K easy,nonn

%O 1,2

%A William A. Berry (waberr2(AT)uky.edu), Dec 21 2006

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Last modified June 24 10:02 EDT 2019. Contains 324323 sequences. (Running on oeis4.)