A084479 Number of fault-free tilings of a 5 X 3n rectangle with right trominoes.

72, 384, 3360, 21504, 163968, 1136640, 8283648, 58791936, 423121920, 3022872576, 21679875072, 155169515520, 1111792499712, 7961492434944, 57028930483200, 408439216748544, 2925470825868288, 20952944438968320, 150073631759459328, 1074876158496638976

Offset: 2

Author

Ralf Stephan, May 27 2003

Keywords

• nonn
• easy

Comments

A tromino is a 3-celled L-shaped piece (a 2 X 2 square with one of the four cells omitted). - N. J. A. Sloane, Mar 28 2017

Fault-free tilings are those where the only straight interface is at the left and right end. Thus a(n) <= A084478(n).

Links

• Colin Barker, Table of n, a(n) for n = 2..1000
• M. Aanjaneya and S. P. Pal, Faultfree tromino tilings of rectangles, arXiv:math/0610925 [math.CO], 2006.
• C. Moore, Some Polyomino Tilings of the Plane, arXiv:math/9905012 [math.CO], 1999.
• Index entries for linear recurrences with constant coefficients, signature (2,31,40,20).

Crossrefs

Cf. A084478, A084477, A084480, A084481.

Programs

Mathematica

LinearRecurrence[{2, 31, 40, 20}, {72, 384, 3360, 21504}, 20] (* Jean-François Alcover, Jan 07 2019 *)

PARI

Vec(24*x^2*(3 + 10*x + 15*x^2) / (1 - 2*x - 31*x^2 - 40*x^3 - 20*x^4) + O(x^30)) \\ Colin Barker, Mar 28 2017

Formula

G.f.: 24*z^2*(3 + 10*z + 15*z^2) / (1 - 2*z - 31*z^2 - 40*z^3 - 20*z^4).

a(n) = 2*a(n-1) + 31*a(n-2) + 40*a(n-3) + 20*a(n-4) for n > 5. - Colin Barker, Mar 28 2017