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

1,2

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.

Links

Table of n, a(n) for n=1..13.

Denis Cazor, Algorithme en Français

Denis Cazor, Algorithm in English

Chyanog, A Chinese web page where the problem was posed.

International Mathematical Olympiad, Problem 3 of IMO 2018.

Example

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].

Crossrefs

Cf. A035312, A035313.

Sequence in context: A177100 A265071 A330910 * A209231 A137358 A143963

Adjacent sequences: A226236 A226237 A226238 * A226240 A226241 A226242

Keyword

nonn,hard,more

Author

Yi Yang, Jun 01 2013

Extensions

a(12) from Yi Yang, Mar 04 2015

a(13) from Denis Cazor, Aug 01 2022

Status

approved