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A134628 Sum-fill array starting with (2,1). 3
2, 1, 2, 3, 1, 2, 5, 3, 4, 1, 2, 7, 5, 8, 3, 4, 1, 2, 9, 7, 12, 5, 13, 8, 11, 3, 4, 1, 2, 11, 9, 16, 7, 19, 12, 17, 5, 18, 13, 21, 8, 14, 3, 4, 1, 2, 13, 11, 20, 9, 25, 16, 23, 7, 26, 19, 31, 12, 29, 17, 22, 5, 18, 34, 21, 8, 14, 3, 4, 1, 2, 15, 13, 24, 11, 31, 20, 29, 9, 34, 25, 41, 16, 39, 23 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The sequence represents a para-sequence.

REFERENCES

C. Kimberling, Proper self-containing sequences, fractal sequences and para-sequences, preprint, 2007.

LINKS

Table of n, a(n) for n=1..85.

Clark Kimberling, Proper self-containing sequences, fractal sequences and para-sequences, unpublished manuscript, 2007, cached copy, with permission.

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 (2,1) begets (2,3,1) because 3 = 2+1; then

(2,3,1) begets (2,5,3,4,1) by sum-filling, etc.

First 5 rows:

2 1

2 3 1

2 5 3 4 1

2 7 5 8 3 4 1

1 6 5 9 4 1 7 10 3 8 2

CROSSREFS

Cf. A134625, A134626, A134627.

Sequence in context: A178030 A131879 A172288 * A064882 A065158 A181842

Adjacent sequences:  A134625 A134626 A134627 * A134629 A134630 A134631

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Nov 04 2007

STATUS

approved

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Last modified June 2 07:15 EDT 2020. Contains 334767 sequences. (Running on oeis4.)