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

0,3

Comments

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

Links

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

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 *)

Crossrefs

Cf. A053414, A053415, A053416, A053417.

Bisections: A000328 and A036704.

Sequence in context: A089217 A166049 A334214 * A332571 A023382 A314793

Adjacent sequences: A053408 A053409 A053410 * A053412 A053413 A053414

Keyword

easy,nonn

Author

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

Status

approved