# [seqfan] Re: Partition into two relatively prime parts?

Alex M timeroot.alex at gmail.com
Sun Jul 3 04:37:05 CEST 2011

```I don't see the connection between these two sequences. The only thing it
says is, "Equal sums is A023022(n+2)". What does this even mean?

~6 out of 5 statisticians say that the
number of statistics that either make
no sense or use ridiculous timescales
at all has dropped over 164% in the
last 5.62474396842 years.

On Sat, Jul 2, 2011 at 5:38 PM, Ron Hardin <rhhardin at att.net> wrote:

> An unpublished companion to (new) http://oeis.org/A109618 mysteriously
> duplicates http://oeis.org/A023022(n+2),  which is
>
>
>  Number of partitions of n into 2 ordered relatively prime  parts. After
> initial
> term, this is the "half-totient" function phi(n)/2.
>
> The unpublished companion is:
>
> Half the number of nXnXn triangular binary arrays with the sum of each
> element's
> NW E SW neighbors equal to the sum of its NE W SE neigbors
>
>  1 1 2 1 3 2 3 2 5 2 6 3 4 4 8 3 9 4 6 5 11 4 10 6 9 6 14 4 15 8 10 8 12 6
> 18 9
> 12 8 20 6 21 10 12 11 23 8 21 10 16 12 26 9 20 12 18 14 29 8 30 15 18 16 24
> 10
> 33 16 22 12 35 12 36 18 20 18 30 12 39 16 27 20 41 12 32 21 28 20 44 12 36
> 22 30
> 23 36 16 48 21 30 20 50 16 51 24 24 26 53 18 54 20 36 24 56 18 44 28 36 29
> 48 16
> 55 30 40 30 50 18 63 32 42
>
> All solutions for 12X12X12 with a(1,1)=0
> .............0........................0........................0..
> ............1.1......................0.0......................0.0..
> ...........0.1.0....................0.0.0....................0.0.0..
> ..........0.0.0.0..................1.1.1.1..................0.0.0.0..
> .........1.1.0.1.1................0.1.1.1.0................0.0.0.0.0..
> ........0.1.0.0.1.0..............0.0.1.1.0.0..............0.0.0.0.0.0..
> .......0.0.0.0.0.0.0............0.0.0.1.0.0.0............0.0.0.0.0.0.0..
> ......1.1.0.1.1.0.1.1..........0.0.0.0.0.0.0.0..........0.0.0.0.0.0.0.0..
> .....0.1.0.0.1.0.0.1.0........1.1.1.1.0.1.1.1.1........0.0.0.0.0.0.0.0.0..
> ....0.0.0.0.0.0.0.0.0.0......0.1.1.1.0.0.1.1.1.0......0.0.0.0.0.0.0.0.0.0..
>
> ...1.1.0.1.1.0.1.1.0.1.1....0.0.1.1.0.0.0.1.1.0.0....0.0.0.0.0.0.0.0.0.0.0..
>
> ..0.1.0.0.1.0.0.1.0.0.1.0..0.0.0.1.0.0.0.0.1.0.0.0..0.0.0.0.0.0.0.0.0.0.0.0..
>
>
>
>
>
>  rhhardin at mindspring.com
> rhhardin at att.net (either)
>
>
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>
> Seqfan Mailing list - http://list.seqfan.eu/
>

```