# [seqfan] Re: A287108: triple patterns.

Alex Meiburg timeroot.alex at gmail.com
Fri May 26 10:29:30 CEST 2017

```We have to rule out 16 other patterns (out of the total 27). Any "2" must
be followed a 1 (as this is its only production rule), so this rules out
and {x,2,{0,2}}, {2,{0,2},x}. These each have 6 possibilities, but they
have {2,2,{0,2}} in common, so between them we've ruled out 10 patterns.

Every 1 must be preceded by a 2 or followed by a 0, so the 4 patterns of
{{0,1},1,{1,2}} are ruled out.

Any instances of {0,0,0} must have the second and third positions generated
by 2's, which would also require a "22" in its predecessor, so that's also
ruled out. Similarly, {0,0,1} would require the second to come from a "2"
and the third position to come from a "0", so the predecessor would require
a "20", so that's ruled out.

That completes the enumeration.

-- Alexander Meiburg

On Mon, May 22, 2017 at 5:15 AM, zak seidov via SeqFan <
seqfan at list.seqfan.eu> wrote:

> A287108:
> Only 11 distinct triple patterns:
> {0, 0, 2}, {0, 1, 0}, {0, 2, 1}, {1, 0, 0}, {1, 0, 1}, {1, 0, 2}, {1, 1,
> 0}, {1, 2, 1}, {2, 1, 0}, {2, 1, 1}, {2, 1, 2}. Any proof that other
> 3-patterns not possible?
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>

```