cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

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

Keywords

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)

Examples

			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.

Links

Crossrefs

Cf. A124623, A120883, A036704.

Formula

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

Extensions

Data corrected by Sean A. Irvine, Sep 02 2021
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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