|
|
A051233
|
|
Number of unit squares at least 50% covered by a circle inscribed in an integer square of size n X n.
|
|
3
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
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
|
|
|
FORMULA
|
|
|
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
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
Joe K. Crump (joecr(AT)carolina.rr.com)
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|