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A368465
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Number of even terms in each row of the iterates of the Christmas tree pattern map (A367508).
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4
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1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 2, 1, 4, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 5, 1, 1, 2, 1, 1, 2, 1, 2, 1, 4, 1, 1, 2, 1, 1, 2, 1, 2, 1, 4, 1, 1, 2, 1, 2, 1, 4, 1, 2, 1, 4, 1, 4, 1, 6, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3
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OFFSET
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1,5
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COMMENTS
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See A367508 for the description of the Christmas tree patterns, references and links.
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LINKS
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EXAMPLE
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The first 4 tree pattern orders are shown below (left), with the corresponding number of even terms on the right.
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Order 1: |
0 1 | 1
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Order 2: |
10 | 1
00 01 11 | 1
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Order 3: |
100 101 | 1
010 110 | 2
000 001 011 111 | 1
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Order 4: |
1010 | 1
1000 1001 1011 | 1
1100 | 1
0100 0101 1101 | 1
0010 0110 1110 | 3
0000 0001 0011 0111 1111 | 1
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MATHEMATICA
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With[{imax=8}, Map[Total, Map[Mod[FromDigits[#]+1, 2]&, NestList[Map[Delete[{If[Length[#]>1, Map[#<>"0"&, Rest[#]], Nothing], Join[{#[[1]]<>"0"}, Map[#<>"1"&, #]]}, 0]&], {{"0", "1"}}, imax-1], {3}], {2}]] (* Generates terms up to order 8 *)
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PROG
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(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(b[-1] == '0' for b 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))]))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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