# [seqfan] Partition into two relatively prime parts?

Ron Hardin rhhardin at att.net
Sun Jul 3 02:38:21 CEST 2011

```An unpublished companion to (new) http://oeis.org/A109618 mysteriously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The unpublished companion is: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)

```