An Integer Sequence

Antreas P. Hatzipolakis xpolakis at
Sun Apr 30 02:00:13 CEST 2000

In the journal _Parabola_ (v. 20, no. 2, 1984, p. 27, #Q607) appeared the
following problem:

  A number of ellipses are drawn in the plane, any two of them intersecting
  in 4 points. No three of the curves are concurrent. Three such ellipses
  divide the plane into 14 regions (including the unbounded region lying
  outside of all the ellipses). Into how many regions would the plane be
  divided if 10 ellipses were drawn?

For n ellipses the formula is:  2(n^2 - n + 1)
So, we have the integer sequence: 2, 6, 14, 26, 42, ......

In EIS there is the sequence: 1, 5, 13, 25, 41, ......

ID Number: A001844 (Formerly M3826 and N1567)
Sequence:  1,5,13,25,41,61,85,113,145,181,221,265,313,365,421,481,545,
Name:      Centered square numbers: 2n(n+1)+1. Also, consider all Pythagorean
           triples (X,Y,Z=Y+1) ordered by increasing Z, sequence gives Z values.


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