A047077 Number of pairs of integers (x,y) with n^2 <= x^2+y^2 <= (n+1)^2.

5, 12, 20, 24, 36, 44, 40, 52, 60, 68, 72, 68, 92, 96, 100, 100, 108, 120, 124, 132, 128, 148, 140, 144, 172, 180, 180, 168, 180, 204, 192, 212, 204, 220, 240, 212, 244, 232, 268, 260, 248, 276, 268, 292, 288, 276, 300, 296, 316, 324, 348, 336, 324, 348, 336

Offset: 0

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 26 2000

Keywords

• easy
• nice
• nonn

Comments

Number of integer Cartesian grid points covered by a ring around the origin with width 1 and outer radius n. Also, number of Gaussian integers z=a+bi satisfying n-1 <= |z| <= n. - Ralf Stephan, Nov 28 2013

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Index entries for Gaussian integers and primes

Crossrefs

Cf. A000328, A051132, A077770.

Programs

Mathematica

a[n_] := Sum[SquaresR[2, k], {k, n^2, (n+1)^2}]; Table[a[n], {n, 0, 54}] (* Jean-François Alcover, Oct 15 2012 *)

Formula

a(n) = A000328(n+1) - A051132(n).