A136561 Triangle read by rows: n-th diagonal (from the right) is the sequence of (signed) differences between pairs of consecutive terms in the (n-1)th diagonal. The rightmost 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.

1, 2, 3, 4, 6, 9, -5, -1, 5, 14, 13, 8, 7, 12, 26, -30, -17, -9, -2, 10, 36, 75, 45, 28, 19, 17, 27, 63, -200, -125, -80, -52, -33, -16, 11, 74, 524, 324, 199, 119, 67, 34, 18, 29, 103, -1299, -775, -451, -252, -133, -66, -32, -14, 15, 118

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.)

Links

Table of n, a(n) for n=1..55.

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 rightmost 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 rightmost element of row 4.
Checking 11,12,13,14; 14 is the smallest value that can be the rightmost element of row 4 and not have any elements of row 4 occur earlier in the triangle.

Crossrefs

Cf. A035312, A136562, A136563.

Sequence in context: A124058 A274423 A118080 * A112868 A111792 A113197

Adjacent sequences: A136558 A136559 A136560 * A136562 A136563 A136564

Keyword

sign,tabl

Author

Leroy Quet, Jan 06 2008

Extensions

Rows 7-10 from Andrey Zabolotskiy, May 29 2017

Status

approved