A368463 Parity of the iterates of the Christmas tree pattern map (A367508), read by rows.

0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1

Offset

1

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).

Formula

a(n) = A367508(n) mod 2.

Maple

The first 4 tree pattern orders are shown below (left), with the corresponding parity on the right.
.
Order 1:                        |
              0  1              |      0  1
                                |
Order 2:                        |
               10               |        0
           00  01  11           |     0  1  1
                                |
Order 3:                        |
            100  101            |      0  1
            010  110            |      0  0
       000  001  011  111       |   0  1  1  1
                                |
Order 4:                        |
              1010              |        0
        1000  1001  1011        |     0  1  1
              1100              |        0
        0100  0101  1101        |     0  1  1
        0010  0110  1110        |     0  0  0
  0000  0001  0011  0111  1111  |  0  1  1  1  1
.

Mathematica

With[{imax=6}, Map[Mod[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[-1]), 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(), 94))) # Michael S. Branicky, Dec 25 2023

Crossrefs

Cf. A367508, A367562, A368464, A368465.

Sequence in context: A245938 A176405 A084091 * A080846 A082401 A157238

Adjacent sequences: A368460 A368461 A368462 * A368464 A368465 A368466

Keyword

nonn,tabf

Author

Paolo Xausa, Dec 25 2023

Status

approved