A367562 Iterates of the Christmas tree pattern map (A367508), read by rows and converted to decimal.

0, 1, 2, 0, 1, 3, 4, 5, 2, 6, 0, 1, 3, 7, 10, 8, 9, 11, 12, 4, 5, 13, 2, 6, 14, 0, 1, 3, 7, 15, 20, 21, 18, 22, 16, 17, 19, 23, 24, 25, 10, 26, 8, 9, 11, 27, 12, 28, 4, 5, 13, 29, 2, 6, 14, 30, 0, 1, 3, 7, 15, 31, 42, 40, 41, 43, 44, 36, 37, 45, 34, 38, 46, 32, 33, 35, 39, 47

Offset

1,3

Comments

See A367508 for the description of the Christmas tree patterns, references and links.

Links

Paolo Xausa, Table of n, a(n) for n = 1..8190 (first 12 orders, flattened).

Example

The first 4 tree pattern orders are shown below (on the right their elements are converted to decimal: the present sequence is obtained by reading the right half of the diagram left to right, top to bottom).
The sequence of the terms in chains of length 1 (marked with asterisks) coincides with the positive terms of A014486.
.
Order 1:                        |
              0  1              |      0  1
                                |
Order 2:                        |
               10               |        2*
           00  01  11           |     0  1  3
                                |
Order 3:                        |
            100  101            |      4  5
            010  110            |      2  6
       000  001  011  111       |   0  1  3  7
                                |
Order 4:                        |
              1010              |       10*
        1000  1001  1011        |     8  9 11
              1100              |       12*
        0100  0101  1101        |     4  5 13
        0010  0110  1110        |     2  6 14
  0000  0001  0011  0111  1111  |  0  1  3  7 15
.

Mathematica

With[{imax=6}, Map[FromDigits[#, 2]&, NestList[Map[Delete[{If[Length[#]>1, Map[#<>"0"&, Rest[#]], Nothing], Join[{#[[1]]<>"0"}, Map[#<>"1"&, #]]}, 0]&], {{"0", "1"}}, imax-1], {3}]] (* Generates terms up to order 6 *)

Prog

(Python)
from itertools import islice
from functools import reduce
def uniq(r): return reduce(lambda u, e: u if e in u else u+[e], r, [])
def agen():  # generator of terms
    R = [["0", "1"]]
    while R:
        r = R.pop(0)
        yield from map(lambda b: int(b, 2), r)
        if len(r) > 1: R.append(uniq([r[k]+"0" for k in range(1, len(r))]))
        R.append(uniq([r[0]+"0", r[0]+"1"] + [r[k]+"1" for k in range(1, len(r))]))
print(list(islice(agen(), 77))) # Michael S. Branicky, Nov 23 2023

Crossrefs

Cf. A014486, A367508, A367555, A367726, A367951, A367953, A368400, A368431.

Sequence in context: A134405 A091612 A253672 * A213861 A355173 A108458

Adjacent sequences: A367559 A367560 A367561 * A367563 A367564 A367565

Keyword

nonn,base,tabf,look

Author

Paolo Xausa, Nov 23 2023

Status

approved