A053411 Circle numbers (version 1): a(n)= number of points (i,j), i,j integers, contained in a circle of diameter n, centered at the origin.

1, 1, 5, 9, 13, 21, 29, 37, 49, 69, 81, 97, 113, 137, 149, 177, 197, 225, 253, 293, 317, 349, 377, 421, 441, 489, 529, 577, 613, 665, 709, 749, 797, 861, 901, 973, 1009, 1085, 1129, 1201, 1257, 1313, 1373, 1457, 1517, 1597, 1653, 1741, 1793, 1885, 1961

Offset: 0

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 10 2000

Keywords

• easy
• nonn

Comments

a(n)/(n/2)^2 -> Pi.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A053414, A053415, A053416, A053417.

Bisections: A000328 and A036704.

Programs

Mathematica

a[n_] := (m = Ceiling[n/2]; Sum[Boole[i^2 + j^2 <= n^2/4], {i, -m, m}, {j, -Ceiling @ Sqrt[ m^2 - i^2 ], Ceiling @ Sqrt[ m^2 - i^2 ]}]); Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Jun 06 2013 *)