# [seqfan] Re: near duplicates A132209 and A142463

Michael Porter ic_designer at verizon.net
Sat Nov 14 10:40:38 CET 2009

```Well, on the other hand, the only reason x=0 is in A132209 but not A142463 is that the left-hand side 2x^3 + 3x^2 in the definition of A132209 is multiplied through by x^2, which seems somewhat arbitrary.  If the defining equation were 2x + 3 = y^2, then the sequences would be identical.

- Michael

--- On Fri, 11/13/09, franktaw at netscape.net <franktaw at netscape.net> wrote:

From: franktaw at netscape.net <franktaw at netscape.net>
Subject: [seqfan] Re: near duplicates A132209 and A142463
To: seqfan at list.seqfan.eu
Date: Friday, November 13, 2009, 2:26 PM

I'm OK with these staying separate.  But there are several problems
with A132209:

(1) The name.  The sequence doesn't "allow us to find the X values" for
2X^3 + 3X^2 = Y^2; it IS the X values.  (This unfortunate phrasing
seems to be repeated in a number of other sequences.  Sigh.)
(2) The formula 2*n^2 + 6n + 3 is off by 1; it should be 2n^2 + 2n - 1.
Likewise, the formula for the Y values should be (2n^2 + 2n - 1)(2n-1).
(3) The comment from Vincenzo Librandi doesn't belong here.
Essentially the same comment is in A142463, which is where it belongs.

And, of course, if both are kept, they should reference each other
("essentially the same as ...").

-----Original Message-----
From: Max Alekseyev <maxale at gmail.com>

A132209 and A142463 are the same except of the first term. In both
cases the first terms seems to be rather out of the context and can be
eliminated by restricting sequence to positive elements or shifting
the offset by 1.
Should these two sequences be merged?
Max

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