A321028 a(n) = 6 + round(n^3) - (minimal number of squares in a dissection of an (n) X (n+1) oblong into squares).

5, 4, 3, 3, 3, 3, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Ed Pegg Jr, Oct 26 2018

Keywords

• hard
• sign

Comments

After a(18) = 2, all terms through a(387) are in (-1,0,1). The first known term outside of this range is a(969) >= 2.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..387 (calculated from the b-file at A279317)
• Bertram Felgenhauer, Filling Rectangles with Integer-Sided Squares.
• Ed Pegg Jr, Minimally Squared Rectangles.
• Ed Pegg Jr, Oblongs into minimal squares, StackExchange, Dec 13 2016.

Crossrefs

Cf. A105209, A279317.

Formula

a(n) = 6 + A105209(n) - A279317(n).