Sequence A112088 Motivation and Example?

[Max]

On 6/9/06, Graeme McRae <g_m at mcraefamily.com> wrote:

> It took me quite some time to understand how Ranier Rosenthal is counting
> rounds, before I obtained A112088 as the number of rounds necessary to kill
> all but one of n players of the Josephus Game with every third man out.  I
> first tried using Hugo Pfoertner's idea where the final survivor counts the
> times he was passed by the executioner including the final rendezvous.  But
> that method gives an entirely different sequence (A005428:
> 1,2,3,4,6,9,14,21,31,47,70,105,158,...).

I've also ended up with this exactly sequence in my computations.

> Then I realized it's the last
> *victim* who counts the number of times he was passed, including the final
> unfortunate rendezvous.  Presumably, he gasps the number with his last
> breath as he falls to the ground.  The last victim counts either the same
> number or one larger than the survivor, depending on where he stood
> initially, relative to the survivor.

I still do not see how A112088 appears here. Could you please clarify
a little bit further?

Thanks,
Max