A053414 Circle numbers (version 2): a(n) is the number of points (i,j), i,j integers, contained in a circle of diameter n, centered at (0, 1/2).

0, 2, 2, 8, 12, 22, 26, 40, 48, 62, 78, 96, 108, 134, 154, 180, 196, 230, 250, 280, 312, 346, 378, 412, 452, 494, 526, 576, 612, 658, 698, 756, 800, 850, 906, 964, 1012, 1074, 1130, 1196, 1252, 1322, 1378, 1448, 1516, 1594, 1654, 1732, 1808, 1882, 1954

Offset

0,2

Comments

Lim_{n->infinity} a(n)/n^2 = Pi/4.

Links

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

Mathematica

a[n_] := (m = Ceiling[n/2]; Sum[ Boole[ n > 2*i && 2*i+n > 0 && n^2 - 4*i^2 + 4*j - 4*j^2 - 1 >= 0 ], {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. A053411, A053415, A053416, A053417.

Sequence in context: A046690 A008828 A254219 * A189837 A274409 A302118

Adjacent sequences: A053411 A053412 A053413 * A053415 A053416 A053417

Keyword

easy,nonn

Author

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

Status

approved