A255809 Infinite tree (flattened) generated as follows: generation g(1) = (1); thereafter, putting h = 2^n, each (1,x(2),...,x(h)) in generation g(n) has 1st and 2nd offspring, namely (1,x(2),...,x(h),x(h)+1) and (1,x(2),...,x(h),x(h)+2).

1, 1, 2, 1, 3, 1, 2, 3, 1, 2, 4, 1, 3, 4, 1, 3, 5, 1, 2, 3, 4, 1, 2, 3, 5, 1, 2, 4, 5, 1, 2, 4, 6, 1, 3, 4, 5, 1, 3, 4, 6, 1, 3, 5, 6, 1, 3, 5, 7, 1, 2, 3, 4, 5, 1, 2, 3, 4, 6, 1, 2, 3, 5, 6, 1, 2, 3, 5, 7, 1, 2, 4, 5, 6, 1, 2, 4, 5, 7, 1, 2, 4, 6, 7, 1, 2

Offset

1,3

Comments

Generation n consists of 2^(n-1) increasing n-tuples that have maximal gapsize 2.

Links

Clark Kimberling, Table of n, a(n) for n = 1..4000

Example

generation g(1) = (1);
g(2) = (1,2), (1,3);
g(3) = (1,2,3), (1,2,4), (1,3,4), (1,3,5);
g(4) = (1,2,3,4), (1,2,3,5), (1,2,4,5), (1,2,4,6), (1,3,4,5), (1,3,4,6), (1,3,5,6), (1,3,5,7).

Mathematica

z = 5; t[n_] := t[n] = Join[{{First[#]}}, Rest[#]] &[Sort[Flatten[NestList[Map[Flatten, Transpose[Map[Flatten[#, 1] &, {{#, #}, {1 + Map[Last, #], 2 + Map[Last, #]}}]]] &, 1(*seed*), #], 1]] &[n(*iterations*)]]
Column[Table[t[n], {n, 1, z}]] (* 1st z generations *)
Flatten[t[6]] (* A255809,  Peter J. C. Moses, Mar 05 2015 *)

Crossrefs

Cf. A255810.

Sequence in context: A325521 A275875 A105497 * A332604 A132662 A279782

Adjacent sequences: A255806 A255807 A255808 * A255810 A255811 A255812

Keyword

nonn,easy

Author

Clark Kimberling, Mar 09 2015

Status

approved