A051233 Number of unit squares at least 50% covered by a circle inscribed in an integer square of size n X n.

1, 4, 9, 12, 21, 32, 37, 52, 69, 80, 97, 112, 137, 156, 177, 208, 225, 256, 293, 316, 349, 384, 421, 448, 489, 540, 577, 616, 665, 716, 749, 812, 861, 912, 973, 1020, 1085, 1124, 1201, 1264, 1313, 1396, 1457, 1528, 1597, 1664, 1741, 1804, 1885, 1976, 2053

Offset

1,2

Comments

From Robert G. Wilson v, Mar 20 2017: (Start)

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

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)

Links

Table of n, a(n) for n=1..51.

Sean A. Irvine, Java program (github)

Formula

Conjecture: a(n) <= A124623(n) with equality in most cases. - Sean A. Irvine, Sep 03 2021

Example

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.

Crossrefs

Cf. A124623, A120883, A036704.

Sequence in context: A332225 A186130 A395700 * A124623 A220195 A221355

Adjacent sequences: A051230 A051231 A051232 * A051234 A051235 A051236

Keyword

nonn,more

Author

Joe K. Crump (joecr(AT)carolina.rr.com)

Extensions

Data corrected by Sean A. Irvine, Sep 02 2021

Status

approved