

A226239


Minimum m such that there exists an nrow subtractive triangle with distinct integers in 1..m.


1



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

1,2


COMMENTS

In an nrow subtractive triangle, there are ni+1 integers in the ith 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.
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


EXAMPLE

a(6)=22 because there is a 6row 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



