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A368398 Iterates of the Christmas tree pattern map (A367508), where each row is interpreted as a single binary word and converted to decimal.

%I A368398 #17 Dec 28 2023 15:03:48
%S A368398 1,2,7,37,22,95,10,2203,12,1117,622,4991,661,598,542327,793,346,
%T A368398 271739,412,136637,72158,1154559,42,166507,44,149869,141742,545667567,
%U A368398 50,199795,52,83317,75190,272971255,56,99961,42682,136623867,51004,68474749,35186622,1125971967
%N A368398 Iterates of the Christmas tree pattern map (A367508), where each row is interpreted as a single binary word and converted to decimal.
%C A368398 See A367508 for the description of the Christmas tree patterns, references and links.
%H A368398 Paolo Xausa, <a href="/A368398/b368398.txt">Table of n, a(n) for n = 1..13494</a> (first 15 orders).
%e A368398 The first 4 tree pattern orders of A367508 are shown below (left). In the middle the elements of each row are joined into single words; decimal conversion is on the right.
%e A368398 .
%e A368398 Order 1:                        |                        |
%e A368398               0  1              |           01           |     1
%e A368398                                 |                        |
%e A368398 Order 2:                        |                        |
%e A368398                10               |           10           |     2
%e A368398            00  01  11           |         000111         |     7
%e A368398                                 |                        |
%e A368398 Order 3:                        |                        |
%e A368398             100  101            |         100101         |    37
%e A368398             010  110            |         010110         |    22
%e A368398        000  001  011  111       |      000001011111      |    95
%e A368398                                 |                        |
%e A368398 Order 4:                        |                        |
%e A368398               1010              |          1010          |    10
%e A368398         1000  1001  1011        |      100010011011      |  2203
%e A368398               1100              |          1100          |    12
%e A368398         0100  0101  1101        |      010001011101      |  1117
%e A368398         0010  0110  1110        |      001001101110      |   622
%e A368398   0000  0001  0011  0111  1111  |  00000001001101111111  |  4991
%e A368398 .
%t A368398 With[{imax=7},Map[FromDigits[StringJoin[#],2]&,NestList[Map[Delete[{If[Length[#]>1,Map[#<>"0"&,Rest[#]],Nothing],Join[{#[[1]]<>"0"},Map[#<>"1"&,#]]},0]&],{{"0","1"}},imax-1],{2}]] (* Generates terms up to order 7 *)
%o A368398 (Python)
%o A368398 from itertools import islice
%o A368398 from functools import reduce
%o A368398 def uniq(r): return reduce(lambda u, e: u if e in u else u+[e], r, [])
%o A368398 def agen():  # generator of terms
%o A368398     R = [["0", "1"]]
%o A368398     while R:
%o A368398         r = R.pop(0)
%o A368398         yield int("".join(r), 2)
%o A368398         if len(r) > 1: R.append(uniq([r[k]+"0" for k in range(1, len(r))]))
%o A368398         R.append(uniq([r[0]+"0", r[0]+"1"] + [r[k]+"1" for k in range(1, len(r))]))
%o A368398 print(list(islice(agen(), 42))) # _Michael S. Branicky_, Dec 26 2023
%Y A368398 Cf. A367508, A367555, A367562.
%K A368398 nonn,base
%O A368398 1,2
%A A368398 _Paolo Xausa_, Dec 22 2023