This sequence gives the difference of squares of distance from the origin to the n-th term, in the Peano curve (A163334) and the Hilbert curve (A163357) on an N x N grid. Because the Hilbert curve is based on powers of 4 and the Peano curve on powers of 9, the graph of this sequence contains dramatic swings. [Edited to Peano vs Hilbert by Kevin Ryde, Aug 28 2020]