OFFSET
1,2
COMMENTS
This sequence and A255774 partition the positive integers.
EXAMPLE
To generate the tree of lazy Fibonacci representations as in A095903, start with 1,2. Suffix the next two Fibonacci numbers, getting 1+2, 1+3; 2+3, 2+5. Suffix the next two Fibonacci numbers, getting 1+2+3, 1+2+5, 1+3+5, 1+3+8; 2+3+5, 2+3+8, 2+5+8, 2+5+13. Continue forever. A255773 is the tree of numbers having root (initial summand) 1, and A255774 is the tree of numbers having root (initial summand) 2.
MATHEMATICA
width = 6; t = Map[Total, Fibonacci[Flatten[NestList[Flatten[Map[{Join[#, {Last[#] +1}], Join[#, {Last[#] + 2}]} &, #], 1] &, {{2}, {3}}, width], 1]]](*A095903*)
Map[t[[#]] &, Apply[Range, {2^Range[#] - 1, 3 2^(Range[#] - 1) - 2}]] &[width + 1] (*A255773*)
Map[t[[#]] &, Apply[Range, {3 2^(Range[#] - 1) - 1, 2 (2^Range[#] - 1)}]] &[width + 1] (*A255774*) (* Peter J. C. Moses, Mar 06 2015 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 06 2015
STATUS
approved