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A136562 Consider the triangle A136561: the n-th diagonal (from the right) is the sequence of (signed) differences between pairs of consecutive terms in the (n-1)th diagonal. The right-most diagonal (A136562) is defined: A136562(1)=1; A136562(n) is the smallest integer > A136562(n-1) such that any (signed) integer occurs at most once in the triangle A136561. 3
1, 3, 9, 14, 26, 36 (list; graph; refs; listen; history; internal format)
OFFSET

1,2

COMMENTS

Requiring that the absolute values of the differences in the difference triangle only occur at most once each leads to the Zorach additive triangle. (See A035312.) The rightmost diagonal of the Zorach additive triangle is A035313.

EXAMPLE

The triangle begins:

1,

2,3,

4,6,9,

-5,-1,5,14,

13,8,7,12,26,

-30,-17,-9,-2,10,36.

Example:

Considering the right-most value of the 4th row: Writing a 10 here instead, the first 4 rows of the triangle become:

1

2,3

4,6,9

-9,-5,1,10

But 1 already occurs earlier in the triangle. So 10 is not the right-most element of row 4.

Checking 11,12,13,14; 14 is the smallest value that can be the right-most element of row 4 and not have any elements of row 4 occur earlier in the triangle. So A136562(4) = 13.

CROSSREFS

Cf. A035313, A136561, A136563.

Sequence in context: A001968 A111907 A195972 * A197274 A100785 A175351

Adjacent sequences:  A136559 A136560 A136561 * A136563 A136564 A136565

KEYWORD

more,nonn

AUTHOR

Leroy Quet Jan 06 2008

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Last modified February 16 02:30 EST 2012. Contains 205860 sequences.