A255810 Infinite tree (flattened) generated as follows: generation g(1) = (1); thereafter, putting h = 3^n, each (1,x(2),...,x(h)) in generation g(n) has 1st, 2nd, and 3rd offspring, namely (1,x(2),...,x(h),x(h)+1), (1,x(2),...,x(h),x(h)+2) and (1,x(2),...,h(h),x(h)+3).

1, 1, 2, 1, 3, 1, 4, 1, 2, 3, 1, 2, 4, 1, 2, 5, 1, 3, 4, 1, 3, 5, 1, 3, 6, 1, 4, 5, 1, 4, 6, 1, 4, 7, 1, 2, 3, 4, 1, 2, 3, 5, 1, 2, 3, 6, 1, 2, 4, 5, 1, 2, 4, 6, 1, 2, 4, 7, 1, 2, 5, 6, 1, 2, 5, 7, 1, 2, 5, 8, 1, 3, 4, 5, 1, 3, 4, 6, 1, 3, 4, 7, 1, 3, 5, 6

Offset

1,3

Comments

Generation n consists of 3^(n-1) increasing n-tuples that have maximal gapsize 3.

Links

Clark Kimberling, Table of n, a(n) for n = 1..7000

Example

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

Mathematica

width = 3; z = 3; t[n_] := t[n] = NestList[Sort[Flatten[Table[Map[Join[#, {m + Last[#]}] &, #], {m, width}], 1]] &, {{1}}, n]
Column[Table[t[n], {n, 1, z}]] (*1st z generations*)
u = Flatten[t[4]] (* Peter J. C. Moses, Mar 09 2015 *)

Crossrefs

Cf. A255809.

Sequence in context: A335286 A064839 A347103 * A210256 A332422 A229944

Adjacent sequences: A255807 A255808 A255809 * A255811 A255812 A255813

Keyword

nonn,easy

Author

Clark Kimberling, Mar 09 2015

Status

approved