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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 (list; graph; refs; listen; history; text; internal format)
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

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

Index entries for Gaussian integers and primes

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-Fran├žois Alcover, Oct 15 2012 *)

CROSSREFS

Cf. A000328, A051132, A077770.

Sequence in context: A017041 A139692 A099192 * A326663 A086570 A270333

Adjacent sequences:  A047074 A047075 A047076 * A047078 A047079 A047080

KEYWORD

easy,nice,nonn

AUTHOR

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

STATUS

approved

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Last modified October 16 02:52 EDT 2019. Contains 328038 sequences. (Running on oeis4.)