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.

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, 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

Offset

1,2

Links

Rajan Murthy, Table of n, a(n) for n = 1..2623

Formula

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

Example

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)).

Crossrefs

First differences of A232499.

Radii are the square roots of A000404.

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.

Sequence in context: A245225 A214860 A263649 * A160242 A043529 A201219

Adjacent sequences: A229901 A229902 A229903 * A229905 A229906 A229907

Keyword

nonn

Author

Rajan Murthy and Vale Murthy, Dec 19 2013

Status

approved