[seqfan] More (and more) fractal trees - and erasures

[Eric Angelini]

Hello SeqFans,

Consider this fractal tree: to recover S, you have to erase here all 3-consecutive integers chunks in S {that is [n(i),n(i+1),n(i+2)], for instance [0,1,2] or [3,4,5] or [6,7,8], etc.} 

S = 0,1,2,0,1,3,4,5,2,0,1,3,4,6,7,8,5,2,0,1,3,4,6,7,9,10,11,8,5,2,0,1,3,4,6,7,9,10,12,13,14,11,8,5,2,0,1,3,4,6,7,9,10,12,13,15,16,17,14,11,8,5,2,0,1,3,4,6,7,9,10,12,13,15,16,18,19,20,17,14,11,8,5,2,0,1,3,4,6,7,9,10,12,13,15,16,18,19,21,22,23,20,17,14,11,8,5,2,...

The pattern is quite obvious - at each step you reproduce the previous one, inserting between n(i+1) and n(i+2) the next triplet [n(i+k), n(i+k+1), n(i+k+2)] :

                                    [0,1,2],
                                0,1,[3,4,5],2,
                            0,1,3,4,[6,7,8],5,2,
                       0,1,3,4,6,7,[9,10,11],8,5,2,
                  0,1,3,4,6,7,9,10,[12,13,14],11,8,5,2,
            0,1,3,4,6,7,9,10,12,13,[15,16,17],14,11,8,5,2,
      0,1,3,4,6,7,9,10,12,13,15,16,[18,19,20],17,14,11,8,5,2,
0,1,3,4,6,7,9,10,12,13,15,16,18,19,[21,22,23],20,17,14,11,8,5,2,...

Best,
É.