OFFSET
1,2
COMMENTS
The sequence represents the para-sequence in which the "final ordering" << is given by 1 << ... << 4 << 3 << 2.
REFERENCES
Clark Kimberling, Proper self-containing sequences, fractal sequences and para-sequences, preprint, 2007.
LINKS
Clark Kimberling, Self-Containing Sequences, Selection Functions, and Parasequences, J. Int. Seq. Vol. 25 (2022), Article 22.2.1.
FORMULA
Row n>=2 is produced from row n by the sum-fill operation, defined on an arbitrary infinite or finite sequence x = (x(1), x(2), x(3), ...) by the following two steps: Step 1. Form the sequence x(1), x(1)+x(2), x(2), x(2)+x(3), x(3), x(3)+x(4), ...; i.e., fill the space between x(n) and x(n+1) by their sum. Step 2. Delete duplicates; i.e., letting y be the sequence resulting from Step 1, if y(n+h)=y(n) for some h>=1, then delete y(n+h).
EXAMPLE
The initial row (1,2) begets (1,3,2) because 3 = 1+2.
Then (1,3,2) begets (1,4,3,5,2) by sum-filling, etc.
First 5 rows:
1 2
1 3 2
1 4 3 5 2
1 5 4 7 3 8 2
1 6 5 9 4 1 7 10 3 8 2
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Nov 04 2007
STATUS
approved