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A047077
Number of pairs of integers (x,y) with n^2 <= x^2+y^2 <= (n+1)^2.
3
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
0,1
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
FORMULA
a(n) = A000328(n+1) - A051132(n).
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 *)
CROSSREFS
KEYWORD
easy,nice,nonn
AUTHOR
Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 26 2000
STATUS
approved