This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A362144 #13 Apr 12 2023 12:27:23
%S A362144 1,1,2,4,6,12,24,40,80,160,280,560,1120,2240,4480,10080,20160,40320,
%T A362144 88704,177408,354816,768768,1537536,3075072,6589440,13178880,26357760,
%U A362144 56010240,112020480,224040960,504092160,1064194560,2128389120,4729753600,9932482560
%N A362144 Maximum number of ways in which a set of integer-sided squares can tile an n X 3 rectangle.
%H A362144 Pontus von Brömssen, <a href="/A362144/b362144.txt">Table of n, a(n) for n = 0..2000</a>
%F A362144 a(n) = max_{3*i+2*j<=n} C(i,j,n-3*i-2*j)*2^j, where C(i,j,k) is the trinomial coefficient (i+j+k)!/(i!*j!*k!). (i and j correspond to the number of squares of side lengths 3 and 2, respectively.)
%Y A362144 Third column of A362142.
%Y A362144 Cf. A002478, A361219 (rectangular pieces).
%K A362144 nonn
%O A362144 0,3
%A A362144 _Pontus von Brömssen_, Apr 10 2023