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A229904 Additional unit squares completely encircled in the first quadrant of a Cartesian grid by a circle centered at the origin as the radius squared increases from one sum of two square integers to the next larger sum of two square integers. 2

%I

%S 1,2,1,2,2,2,1,2,2,2,2,1,2,2,2,2,2,3,2,2,2,2,4,2,1,2,2,2,2,4,2,2,2,1,

%T 2,2,2,2,2,2,2,2,2,4,1,4,2,2,4,2,2,2,2,2,2,1,2,2,4,2,2,2,2

%N Additional unit squares completely encircled in the first quadrant of a Cartesian grid by a circle centered at the origin as the radius squared increases from one sum of two square integers to the next larger sum of two square integers.

%H Rajan Murthy, <a href="/A229904/b229904.txt">Table of n, a(n) for n = 1..2623</a>

%F a(n) = A232499(n) - A232499(n-1) for n>1, a(1) = A232499(1).

%e When the radius increases from 0 to sqrt(2), one square is completely encircled (a(1)). When the radius increases from sqrt(2) to sqrt(3), two more squares are encircled (a(2)). When the radius increases from sqrt(45) to sqrt(50), three more squares are encircled(a(18)).

%Y First differences of A232499.

%Y Radii are the square roots of A000404.

%Y The first differences must be odd at positions given in A024517 by proof by symmetry as r^2=2*n^2 is on the x=y line.

%K nonn

%O 1,2

%A _Rajan Murthy_ and _Vale Murthy_, Dec 19 2013

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Last modified September 27 00:14 EDT 2020. Contains 337378 sequences. (Running on oeis4.)