

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
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OFFSET

1,3


COMMENTS

Generation n consists of 3^(n1) increasing ntuples 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



