# [seqfan] Re: A007898 ('Connected with Fibonacci partitions')

David Newman davidsnewman at gmail.com
Fri Apr 23 18:43:07 CEST 2010

```Here's the sequence  which led me to A007898 when I searched for
1,2,3,3,4,4,7,7,6,6,...

How many sequences are there of the following sort.

A= a_1,a_2,a_3,...,a_k has k elements each of which is +1 or -1, and a1=1.
For all positive integers x and y (a_x) (a_y)= a_xy and
The sum of elements a_i , a_2i, a_3i, ...is never greater than 2 in absolute
value, where i is a positive integer.

For example:

There is one sequence of length 1:  +1
I'll abbreviate +1 to + and -1 to - from here on.

There are two of length 2:  + + and + -
There are three of length 3:  + + -,  + - +, + - -
There are three of length 4:  + + - +, + - + +, + - - +

Sequences of this sort are the subject of current research see for example

http://michaelnielsen.org/polymath1/index.php?title=The_Erd%C5%91s_discrepancy_problem

This sequence does not match A007898 for larger values.

The author of that sequence seems to be at the Anatomy department of the
University of Bern in Switzerland.  This much is easy to pick up on the
Internet.  But he still hasn't answered my email.
On Fri, Apr 23, 2010 at 10:01 AM, N. J. A. Sloane <njas at research.att.com>wrote:

> > No appearance of the seq in the paper.
>
> Well, the paper contains a large number of sequences
> that are defined in the text but not explicitly
> evaluated.  Someone might care to work through the
> paper and compute all the sequences - adding new ones to the
> OEIS, extending others.  Perhaps A007898 will emerge.
>
> The paper is on the arXiv.
>
> Neil
>
>
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```