login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Number of ordered pairs of integers (x,y) with n^2 < x^2 + y^2 < (n+1)^2; number of lattice points between circles of radii n and n+1.
4

%I #7 Mar 30 2012 17:22:26

%S 0,4,12,16,20,28,32,44,52,52,56,60,76,80,84,84,92,104,116,116,112,140,

%T 132,136,148,148,164,160,164,180,176,204,196,204,216,196,228,216,252,

%U 236,224,260,260,284,272,260,292,288,308,300,316,312,300,332,320,364

%N Number of ordered pairs of integers (x,y) with n^2 < x^2 + y^2 < (n+1)^2; number of lattice points between circles of radii n and n+1.

%C Note that 2*A077768(n)-a(n)/4 is the characteristic sequence for the Beatty sequence A001951(n).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GausssCircleProblem.html">Gauss's Circle Problem</a>

%F a(n) = A051132(n+1) - A000328(n)

%t Table[Sum[SquaresR[2, k], {k, n^2 + 1, (n + 1)^2 - 1}], {n, 0, 100}]

%Y Cf. A000328, A001951, A051132, A077768.

%K nonn

%O 0,2

%A _T. D. Noe_, Nov 20 2002