This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A367562 #32 Dec 30 2023 14:39:32
%S A367562 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,
%T A367562 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,
%U A367562 0,1,3,7,15,31,42,40,41,43,44,36,37,45,34,38,46,32,33,35,39,47
%N A367562 Iterates of the Christmas tree pattern map (A367508), read by rows and converted to decimal.
%C A367562 See A367508 for the description of the Christmas tree patterns, references and links.
%H A367562 Paolo Xausa, <a href="/A367562/b367562.txt">Table of n, a(n) for n = 1..8190</a> (first 12 orders, flattened).
%e A367562 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).
%e A367562 The sequence of the terms in chains of length 1 (marked with asterisks) coincides with the positive terms of A014486.
%e A367562 .
%e A367562 Order 1: |
%e A367562 0 1 | 0 1
%e A367562 |
%e A367562 Order 2: |
%e A367562 10 | 2*
%e A367562 00 01 11 | 0 1 3
%e A367562 |
%e A367562 Order 3: |
%e A367562 100 101 | 4 5
%e A367562 010 110 | 2 6
%e A367562 000 001 011 111 | 0 1 3 7
%e A367562 |
%e A367562 Order 4: |
%e A367562 1010 | 10*
%e A367562 1000 1001 1011 | 8 9 11
%e A367562 1100 | 12*
%e A367562 0100 0101 1101 | 4 5 13
%e A367562 0010 0110 1110 | 2 6 14
%e A367562 0000 0001 0011 0111 1111 | 0 1 3 7 15
%e A367562 .
%t A367562 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 *)
%o A367562 (Python)
%o A367562 from itertools import islice
%o A367562 from functools import reduce
%o A367562 def uniq(r): return reduce(lambda u, e: u if e in u else u+[e], r, [])
%o A367562 def agen(): # generator of terms
%o A367562 R = [["0", "1"]]
%o A367562 while R:
%o A367562 r = R.pop(0)
%o A367562 yield from map(lambda b: int(b, 2), r)
%o A367562 if len(r) > 1: R.append(uniq([r[k]+"0" for k in range(1, len(r))]))
%o A367562 R.append(uniq([r[0]+"0", r[0]+"1"] + [r[k]+"1" for k in range(1, len(r))]))
%o A367562 print(list(islice(agen(), 77))) # _Michael S. Branicky_, Nov 23 2023
%Y A367562 Cf. A014486, A367508, A367555, A367726, A367951, A367953, A368400, A368431.
%K A367562 nonn,base,tabf,look
%O A367562 1,3
%A A367562 _Paolo Xausa_, Nov 23 2023