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(OddQ[Length[#]] &), {2}]
(see page 358 )
• Flatten[Table[Map[{t, #} &, Fold[Flatten[{#1, #1 + #2}] &, 0, Flatten[2^(Position[ Reverse[IntegerDigits[t, 2]], 1] - 1)]]], {t, 2 n - 1}], 1]
(see page 870 )
• Map[Map[FromDigits[#, 2] &, Transpose[Partition[#, 2]]] &, Position[Nest[{{#, #}, {#}} &, 1, n], 1] - 1]
(see page 509 )
A formatting hack giving the same visual pattern is
DisplayForm[Nest[SubsuperscriptBox[#, #, #] &, "1", n]]