[seqfan] A Xmas fractal tree

Eric Angelini Eric.Angelini at kntv.be
Sat Dec 27 12:08:09 CET 2014


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).





More information about the SeqFan mailing list