A367555 Number of zeros (or ones) in each row of the iterates of the Christmas tree pattern map (A367508).

1, 1, 3, 3, 3, 6, 2, 6, 2, 6, 6, 10, 5, 5, 10, 5, 5, 10, 5, 10, 10, 15, 3, 9, 3, 9, 9, 15, 3, 9, 3, 9, 9, 15, 3, 9, 9, 15, 9, 15, 15, 21, 7, 7, 14, 7, 7, 14, 7, 14, 14, 21, 7, 7, 14, 7, 7, 14, 7, 14, 14, 21, 7, 7, 14, 7, 14, 14, 21, 7, 14, 14, 21, 14, 21, 21, 28

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..13494 (first 15 orders).

Example

The following diagram shows the first 4 tree pattern orders, along with the corresponding number of zeros = number of ones.
.
Order 1:                        |
              0  1              |   1
                                |
Order 2:                        |
               10               |   1
           00  01  11           |   3
                                |
Order 3:                        |
            100  101            |   3
            010  110            |   3
       000  001  011  111       |   6
                                |
Order 4:                        |
              1010              |   2
        1000  1001  1011        |   6
              1100              |   2
        0100  0101  1101        |   6
        0010  0110  1110        |   6
  0000  0001  0011  0111  1111  |  10
.

Mathematica

With[{imax=9}, Map[Total, NestList[Map[Delete[{If[Length[#]>1, Rest[#], Nothing], Join[{First[#]}, #+1]}, 0]&], {{0, 1}}, imax-1], {2}]] (* Generates terms up to order 9 *)

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 sum(e.count("1") for e in 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. A367508, A367562.

Sequence in context: A261450 A100026 A350537 * A100049 A261926 A158315

Adjacent sequences: A367552 A367553 A367554 * A367556 A367557 A367558

Keyword

nonn,base

Author

Paolo Xausa, Nov 22 2023

Status

approved