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

Author

Leroy Quet, Jan 06 2008

Keywords

• sign
• tabl

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.)

Examples

			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.

Extensions

Rows 7-10 from Andrey Zabolotskiy, May 29 2017