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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 09 2015
STATUS
approved