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%I #25 Sep 06 2021 13:30:44
%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
%N Number of unit squares at least 50% covered by a circle inscribed in an integer square of size n X n.
%C From _Robert G. Wilson v_, Mar 20 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). (End)
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a051/A051233.java">Java program</a> (github)
%F Conjecture: a(n) <= A124623(n) with equality in most cases. - _Sean A. Irvine_, Sep 03 2021
%e a(2)=4 because an inscribed circle in a 2 X 2 grid covers at least 50% of each of the unit squares within it.
%Y Cf. A124623, A120883, A036704.
%K nonn,more
%O 1,2
%A Joe K. Crump (joecr(AT)carolina.rr.com)
%E Data corrected by _Sean A. Irvine_, Sep 02 2021
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