A372847 Number of unit squares enclosed by a circle of radius n with an even number of rows and the maximum number of squares in each row.

0, 6, 18, 36, 64, 92, 130, 172, 224, 284, 344, 410, 488, 570, 658, 750, 852, 956, 1072, 1194, 1312, 1450, 1584, 1728, 1882, 2044, 2204, 2372, 2548, 2730, 2916, 3112, 3312, 3520, 3738, 3950, 4184, 4408, 4656, 4900, 5146, 5402, 5670, 5942, 6222, 6492, 6784, 7080, 7382, 7700

Offset

1,2

Comments

Always has an even number of rows (2*n-2) and each row may have an odd or even number of squares.

Symmetrical about the horizontal and vertical axes.

Links

David Dewan, Table of n, a(n) for n = 1..10000

David Dewan, Drawings for n=1..12.

Formula

a(n) = 2*Sum_{k=1..n-1} floor(2*sqrt(n^2 - k^2)).

Example

For n=4
row 1:   5 squares
row 2:   6 squares
row 3:   7 squares
row 4:   7 squares
row 5:   6 squares
row 6:   5 squares
Total = 36

Mathematica

a[n_]:=2 Sum[Floor[2 Sqrt[n^2 - k^2]], {k, n-1}]; Array[a, 50]

Crossrefs

Cf. A136485 (by diameter), A001182 (within quadrant), A136483 (quadrant by diameter), A119677 (even number of rows with even number of squares in each), A125228 (odd number of rows with maximal squares per row), A341198 (points rather than squares).

Sequence in context: A028896 A295026 A034857 * A116367 A225384 A276480

Adjacent sequences: A372844 A372845 A372846 * A372848 A372849 A372850

Keyword

nonn

Author

David Dewan, May 14 2024

Status

approved