A084481 Number of fault-free tilings of a 4 X 2n rectangle with L tetrominoes.

2, 6, 10, 18, 38, 84, 186, 410, 904, 1994, 4398, 9700, 21394, 47186, 104072, 229538, 506262, 1116596, 2462730, 5431722, 11980040, 26422810, 58277342, 128534724, 283492258, 625261858, 1379058440, 3041609138, 6708480134, 14796018708, 32633646554, 71975773242

Offset: 1

Author

Ralf Stephan, May 27 2003

Keywords

• nonn
• easy

Comments

Fault-free tilings are those where the only straight interface is at the left and right end. Thus a(n) <= A084480(n).

If the conjectured G.F. in A183304 is true, then a(n)= 2*A183304(n-1), n>3. - R. J. Mathar, Dec 02 2022

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Nicolas Bělohoubek and Antonín Slavík, L-Tetromino Tilings and Two-Color Integer Compositions, Univ. Karlova (Czechia, 2025). See p. 10.
• C. Moore, [math/9905012] Some Polyomino Tilings of the Plane
• Index entries for linear recurrences with constant coefficients, signature (2,0,1).

Crossrefs

Cf. A084478, A084479, A084480, A084477.

Programs

PARI

Vec(2*x*(1 + x)^2*(1 - x - x^3) / (1 - 2*x - x^3) + O(x^30)) \\ Colin Barker, Mar 28 2017

Formula

G.f.: 2*z*(1+z)^2*(1-z-z^3) / (1-2*z-z^3).

a(n) = 2*a(n-1) + a(n-3) for n>6. - Colin Barker, Mar 28 2017