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

%I A321028 #28 Jul 23 2025 17:23:54
%S A321028 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,
%T A321028 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,
%U A321028 -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
%N A321028 a(n) = 6 + round(n^3) - (minimal number of squares in a dissection of an (n) X (n+1) oblong into squares).
%C A321028 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.
%H A321028 Amiram Eldar, <a href="/A321028/b321028.txt">Table of n, a(n) for n = 1..387</a> (calculated from the b-file at A279317)
%H A321028 Bertram Felgenhauer, <a href="http://int-e.eu/~bf3/squares/">Filling Rectangles with Integer-Sided Squares</a>.
%H A321028 Ed Pegg Jr, <a href="http://demonstrations.wolfram.com/MinimallySquaredRectangles/">Minimally Squared Rectangles</a>.
%H A321028 Ed Pegg Jr, <a href="http://math.stackexchange.com/questions/2057290/oblongs-into-minimal-squares">Oblongs into minimal squares</a>, StackExchange, Dec 13 2016.
%F A321028 a(n) = 6 + A105209(n) - A279317(n).
%Y A321028 Cf. A105209, A279317.
%K A321028 hard,sign
%O A321028 1,1
%A A321028 _Ed Pegg Jr_, Oct 26 2018