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

1, 1, 2, 4, 6, 12, 24, 40, 80, 160, 280, 560, 1120, 2240, 4480, 10080, 20160, 40320, 88704, 177408, 354816, 768768, 1537536, 3075072, 6589440, 13178880, 26357760, 56010240, 112020480, 224040960, 504092160, 1064194560, 2128389120, 4729753600, 9932482560

Offset: 0

Author

Pontus von Brömssen, Apr 10 2023

Keywords

• nonn

Links

• Pontus von Brömssen, Table of n, a(n) for n = 0..2000

Crossrefs

Third column of A362142.

Cf. A002478, A361219 (rectangular pieces).

Formula

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.)