

A134625


Sumfill array starting with (1,2,3,4,...).


3



1, 2, 1, 3, 3, 1, 4, 2, 4, 1, 5, 5, 3, 5, 1, 6, 7, 5, 4, 6, 1, 7, 4, 2, 7, 5, 7, 1, 8, 9, 7, 3, 9, 6, 8, 1, 9, 11, 12, 8, 4, 11, 7, 9, 1, 10, 6, 11, 2, 11, 5, 13, 8, 10, 1, 11, 13, 13, 9, 7, 14, 6
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Every row is a permutation of the positive integers. (Row 2) = A006369. The sequence represents the parasequence in which the "final ordering" << is given by 1 << ... << 4 << 3 << 2. In every row after row n, for each k<=n, k+1 precedes k and all the numbers between k+1 and k exceed k+1.


REFERENCES

C. Kimberling, Proper selfcontaining sequences, fractal sequences and parasequences, preprint, 2007.


LINKS

Table of n, a(n) for n=1..62.
Clark Kimberling, Proper selfcontaining sequences, fractal sequences and parasequences, unpublished manuscript, 2007, cached copy, with permission.


FORMULA

Row 1 is the sequence of positive integers. Row n>=2 is produced from row n by the sumfill 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

Starting with x = row 1, Step 1 gives
y = (1,3,2,5,3,7,4,9,5,11,6,13,...).
Delete the second 3,5,7,... leaving row 2:
(1,3,2,5,7,4,9,11,6,13,...).
Northwest corner:
1 2 3 4 5 6 7 8
1 3 2 5 7 4 9 11
1 4 3 5 2 7 12 11
1 5 4 7 3 8 2 9
1 6 5 9 4 11 7 10.


CROSSREFS

Cf. A134626, A134627, A134628.
Sequence in context: A195915 A219158 A049834 * A325477 A277227 A054531
Adjacent sequences: A134622 A134623 A134624 * A134626 A134627 A134628


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Nov 04 2007


STATUS

approved



