# [seqfan] Re: Philippe Deleham's new tree (and A230871)

Kevin Ryde user42 at zip.com.au
Fri Nov 8 23:06:53 CET 2013

```njasloane at gmail.com (Neil Sloane) writes:
>
> A230871

Since the columns are Fibonacci recurrences they are (eventually) rows
of the Wythoff array A035513.  Perhaps the row number would be of
interest.  Counting the first Wythoff row as 1 (which is the Fibonacci
numbers),

1,8,11,50,18,63,69,338,74,112,90,419,309,409,467,2312,120,456,414,

Eg. Column 2: 3,2,5,7,12,19,31,...=A013655 is Wythoff row 8 beginning
19,31.  The row numbers seem all different, which is to say the columns
are always distinct sequences.  Perhaps that can be had from the tree
definition.

For this "column 2" you have to go down 5 places in the column to get to
the 19,31 start of the Wythoff row.  That distance down seems to be

2,5,5,7,5,7,7,9,7,7,7,9,9,9,9,11,7,9,9,9

Perhaps there's an easy reason they're all odd after the first.  The
Wythoff row of course starts with two numbers which are in Zeckendorf
base (A014417) "xxx1","xxx10", if there's a reason the tree column is an
odd number of entries backwards from such a pair.

(The superseeker crunched for a while but didn't report anything for
either the above.)

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