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Maximum number of unit squares aligned with unit-spaced horizontal lines that can be enclosed by a circle of radius n.
4

%I #54 Aug 01 2024 09:17:41

%S 0,1,8,21,40,65,97,135,180,229,286,350,419,495,575,664,761,860,966,

%T 1079,1200,1326,1458,1595,1741,1892,2050,2213,2383,2558,2741,2930,

%U 3124,3328,3534,3746,3967,4194,4428,4666,4910,5162,5420,5682,5952,6231,6517,6802,7097

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

%C 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]

%C 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

%H P. Erdős and R. L. Graham, <a href="http://dx.doi.org/10.1016/0097-3165(75)90099-0">On packing squares with equal squares</a>, J. Comb. Theory (A), 19 (1975), 119-123.

%H Erich Friedman, <a href="https://erich-friedman.github.io/packing/squincir/">Squares in Circles</a>.

%H Jason Holt, <a href="https://web.archive.org/web/20070905131932/http://lunkwill.org/src/square-in-circle/">Packing squares into circles</a>.

%H Hugo Pfoertner, <a href="/A124484/a124484.pdf">Illustration of a(2)-a(12)</a>, showing results of Jason Holt's C program.

%F a(n) = A374505(2*n). - _David Dewan_, Jul 10 2024

%Y Cf. A374505.

%K nonn

%O 0,3

%A _Jason Holt_, Nov 10 2006

%E a(1) corrected by _David Dewan_, Jun 13 2024

%E Name and definition amended to be consistent with the author's program by _Hugo Pfoertner_, Jul 14 2024

%E a(20) onwards from _David Dewan_, Jul 14 2024