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 A362144 Maximum number of ways in which a set of integer-sided squares can tile an n X 3 rectangle. 3

%I #13 Apr 12 2023 12:27:23

%S 1,1,2,4,6,12,24,40,80,160,280,560,1120,2240,4480,10080,20160,40320,

%T 88704,177408,354816,768768,1537536,3075072,6589440,13178880,26357760,

%U 56010240,112020480,224040960,504092160,1064194560,2128389120,4729753600,9932482560

%N Maximum number of ways in which a set of integer-sided squares can tile an n X 3 rectangle.

%H Pontus von BrÃ¶mssen, <a href="/A362144/b362144.txt">Table of n, a(n) for n = 0..2000</a>

%F 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 Third column of A362142.

%Y Cf. A002478, A361219 (rectangular pieces).

%K nonn

%O 0,3

%A _Pontus von BrÃ¶mssen_, Apr 10 2023

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Last modified February 23 15:29 EST 2024. Contains 370283 sequences. (Running on oeis4.)