[seqfan] Re: Fractal sequence A087088

[Kevin Ryde]

acwacw at gmail.com (Allan Wechsler) writes:
>
> something like "Positive ruler-type
> fractal sequence with 1's in every third position."

Concerning rulers, I've mentioned elsewhere I struck this sequence as
"how far carry propagates when incrementing in base 3/2", which is
ruler-like.

However my base 3/2 is an unusual variant with digits -1/2, 0, +1/2
except highest digit 1, and "integer prefixing" (still integer if
discard least significant digit).  I haven't encountered this elsewhere
and don't know whether the concept is good beyond my own use so-far.

A more straightforward, and more or less equivalent, interpretation is
how far up to the common ancestor of n and n+1 in a certain tree defined
by 2 children for odd and 1 child for even -- counting positions across
each tree row.  Here's a rough picture.

    http://user42.tuxfamily.org/temporary/A087088-tree.pdf

I'll have to try a bigger better picture for something visual.
The descents follow without much trouble from the recurrence formulas,
or Benoit Cloitre's construction.