A124484 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

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

Table of n, a(n) for n=0..48.

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.

FORMULA

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

CROSSREFS

Cf. A374505.

Sequence in context: A279895 A225287 A000567 * A137742 A275874 A190456

Adjacent sequences: A124481 A124482 A124483 * A124485 A124486 A124487