[seqfan] Re: A007898 ('Connected with Fibonacci partitions')
Rainer Rosenthal
r.rosenthal at web.de
Sat Apr 24 00:01:47 CEST 2010
David Newman wrote:
> 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: + + - +, + - + +, + - - +
Sorry, but I don't see, why there should be only four such sequences
of length 6. What's wrong with these six:
1. + + - + + - (discrepancy 2)
2. + + - + - - (discrepancy 2)
3. + - + + + - (discrepancy 2)
4. + - + + - - (discrepancy 1)
5. + - - + + + (discrepancy 2)
6. + - - + - + (discrepancy 1)
They seem to be multiplicative:
a_4 = a_2*a_2 = +1 and a_6 = a_2*a_3.
Cheers,
Rainer
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