An Integer Sequence

Len M. Smiley smiley at math.uaa.alaska.edu
Sun Apr 30 17:44:31 CEST 2000

```Also, A002061 Central polygonal numbers: 1,1,3,7,13,21,... (=n^2 - n + 1).
Perhaps a comment?

On Sun, 30 Apr 2000, Antreas P. Hatzipolakis wrote:

> 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,
>            613,685,761,841,925,1013,1105,1201,1301,1405,1513,1625,1741,
>            1861,1985,2113,2245,2381,2521,2665,2813,2965,3121,3281,3445,
>            3613,3785,3961,4141,4325
> 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.
> [...]
>
>
> Antreas
>
>
>

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