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

1,1

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

Table of n, a(n) for n=1..125.

B. Felgenhauer, Filling Rectangles with Integer-Sided Squares

Ed Pegg Jr, Minimally Squared Rectangles

Ed Pegg Jr on StackExchange, Oblongs into minimal squares, Dec 13 2016.

Formula

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

Crossrefs

Cf. A105209, A279317.

Sequence in context: A276052 A374420 A348340 * A351169 A263356 A061836

Adjacent sequences: A321025 A321026 A321027 * A321029 A321030 A321031

Keyword

hard,sign

Author

Ed Pegg Jr, Oct 26 2018

Status

approved