|
%I #29 Mar 28 2017 14:56:38
%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
|
