[seqfan] Re: A Xmas fractal tree

[Reinhard Zumkeller]

and row sums = A035608, without proof ...

2014-12-27 22:36 GMT+01:00 Reinhard Zumkeller <reinhard.zumkeller at gmail.com>
:

> see https://oeis.org/draft/A253146, some narrative might be nice.
> Best regards
> Reinhard
>
>
> 2014-12-27 21:54 GMT+01:00 Neil Sloane <njasloane at gmail.com>:
>
>> Eric's Christmas Tree sequence is very nice.
>> The one that begins:
>>
>> 1, 2,3, 4,1,5, 6,2,3,7, 8, 9,4,1,5,10, 11,6,2,3,7,12, 13,14, 15,8,16, ...
>>
>> If we call it a fractal tree, not mentioning Christmas,
>> then it could go into the OEIS, I think.
>>
>> Trees are legitimate mathematical shapes to study,
>> just like spirals.
>>
>> Could someone add it (and
>> reply with the A-number, so I can look for it on the editing
>> stack (which is getting very big))?
>>
>> Best regards
>> Neil
>>
>> Neil J. A. Sloane, President, OEIS Foundation.
>> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
>> Phone: 732 828 6098; home page: http://NeilSloane.com
>> Email: njasloane at gmail.com
>>
>>
>> On Sat, Dec 27, 2014 at 6:08 AM, Eric Angelini <Eric.Angelini at kntv.be>
>> wrote:
>>
>> > Hello SeqFans,
>> > Here is a fractal Xmas tree. Many thanks to all contributors who took
>> the
>> > time to read my posts so far – and a happy 2015 to the wonderful OEIS’
>> > staff!
>> > Best,
>> > É.
>> >
>> >
>> >
>> >                                   1,
>> >                                  2,3,
>> >                                 4,1,5,
>> >                                6,2,3,7,
>> >                                   8,
>> >                               9,4,1,5,10,
>> >                             11,6,2,3,7,12,
>> >                                 13,14,
>> >                                15,8,16,
>> >                            17,9,4,1,5,10,18,
>> >                          19,11,6,2,3,7,12,20,
>> >                         21,13,8,4,1,5,9,14,22,
>> >                              23,15,16,24,
>> >                                  25,
>> >                            26,17,10,18,27,
>> >                       28,19,11,6,2,3,7,12,20,29,
>> >                      30,21,13,8,4,1,5,9,14,22,31,
>> >                           32,23,15,16,24,33,
>> >                                 34,35,
>> >                               36,25,37,
>> >                         38,26,17,10,18,27,39,
>> >                    40,28,19,11,6,2,3,7,12,20,29,41,
>> >                   42,30,21,13,8,4,1,5,9,14,22,31,43,
>> >                 44,32,23,15,10,6,2,3,7,11,16,24,33,45,
>> >                46,34,25,17,12,8,4,1,5,9,13,18,26,35,47,
>> >                        48,36,27,19,20,28,37,49,
>> >              50,38,29,21,14,10,6,2,3,7,11,15,22,30,39,51,
>> >             52,40,31,23,16,12,8,4,1,5,9,13,17,24,32,41,53,
>> >                      54,42,33,25,18,26,34,43,55,
>> >                              56,44,45,57,
>> >                                  58,
>> >                                  ...
>> >
>> > Shape:
>> > The width of the tree, at every stage, is given by the tree itself,
>> > starting from the top (the successive widths, starting from the top, are
>> > 1,2,3,4,1,5,6,2,3,7,...)
>> >
>> > Fractality:
>> > If you “peel” the tree, it will reappear – unchanged (to “peel” is to
>> > erase the first and last integer of each layer).
>> >
>> >
>> >
>> > _______________________________________________
>> >
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>> >
>>
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