A226239 Minimum m such that there exists an n-row subtractive triangle with distinct integers in 1..m.

1, 3, 6, 10, 15, 22, 33, 44, 59, 76, 101, 125, 158

Offset: 1

Author

Yi Yang, Jun 01 2013

Keywords

• nonn
• hard
• more

Comments

In an n-row subtractive triangle, there are n-i+1 integers in the i-th row. The integers in the first row are arbitrary. From the next row, the integers are the absolute difference between adjacent integers in the previous row.

Examples

			a(6)=22 because there is a 6-row subtractive triangle with distinct integers in [1..22] as follows:
1:  6 20 22  3 21 13
2: 14  2 19 18  8
3: 12 17  1 10
4:  5 16  9
5: 11  7
6:  4
However, there is no such triangle with distinct integers in [1..21].
		

Links

• Chyanog, A Chinese web page where the problem was posed.
• International Mathematical Olympiad, Problem 3 of IMO 2018.
• Denis Cazor, Algorithme en Français
• Denis Cazor, Algorithm in English

Crossrefs

Cf. A035312, A035313.

Extensions

a(12) from Yi Yang, Mar 04 2015

a(13) from Denis Cazor, Aug 01 2022