A124484 Maximum number of unit squares aligned with unit-spaced horizontal lines that can be enclosed by a circle of radius n.

0, 1, 8, 21, 40, 65, 97, 135, 180, 229, 286, 350, 419, 495, 575, 664, 761, 860, 966, 1079, 1200, 1326, 1458, 1595, 1741, 1892, 2050, 2213, 2383, 2558, 2741, 2930, 3124, 3328, 3534, 3746, 3967, 4194, 4428, 4666, 4910, 5162, 5420, 5682, 5952, 6231, 6517, 6802, 7097

Offset: 0

Author

Jason Holt, Nov 10 2006

Keywords

• nonn

Comments

I don't know how many of these entries have been proved to be optimal. The Erdős-Graham paper shows how subtle such problems can be. - N. J. A. Sloane, Dec 19 2006 [This comment was written before the July 2024 clarifications to the name and definition. - Editors]

In the Erdős-Graham paper and on Erich Friedman's website, the orientation of the squares is not restricted to a position parallel to the axes. - Hugo Pfoertner, Jul 14 2024

Links

• P. Erdős and R. L. Graham, On packing squares with equal squares, J. Comb. Theory (A), 19 (1975), 119-123.
• Erich Friedman, Squares in Circles.
• Jason Holt, Packing squares into circles.
• Hugo Pfoertner, Illustration of a(2)-a(12), showing results of Jason Holt's C program.

Crossrefs

Cf. A374505.

Formula

a(n) = A374505(2*n). - David Dewan, Jul 10 2024

Extensions

a(1) corrected by David Dewan, Jun 13 2024

Name and definition amended to be consistent with the author's program by Hugo Pfoertner, Jul 14 2024

a(20) onwards from David Dewan, Jul 14 2024