Spiral sequences through the integer plane

[Joseph Biberstine]

I'm shocked that these seem to be absent.  Consider the coordinates of a
path spirally traversing the integer plane (principal quadrant or whole)
any of the usual ways.  These all seem to be absent from EIS.  Am I right?

For example, spanning the principal quadrant in this way in either of
the two departures from the origin, for example:
{{0,0},{0,1},{1,1},{1,0},{2,0},{2,1},{2,2},{1,2},{0,2},{0,3}, ...}

Or spiraling in either handedness from any of four departures from the
origin, for example:
{{0,0},{1,0},{1,1},{0,1},{-1,1},{-1,0},{-1,-1},{0,-1},{1,-1},...}

Are these in EIS and if not can you provide a closed formula for the
n-th coordinate in any matter of traversal?

-JRB