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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). 2
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 (list; graph; refs; listen; history; text; internal format)
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]] (* A255810, _Peter J.C.Moses_, Mar 09 2015*)

CROSSREFS

Cf. A255809.

Sequence in context: A241919 A286469 A064839 * A210256 A332422 A229944

Adjacent sequences:  A255807 A255808 A255809 * A255811 A255812 A255813

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 09 2015

STATUS

approved

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Last modified February 24 03:22 EST 2020. Contains 332195 sequences. (Running on oeis4.)