OFFSET
1,1
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) <= A046984(n).
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
M. Aanjaneya and S. P. Pal, Faultfree tromino tilings of rectangles
Index entries for linear recurrences with constant coefficients, signature (6).
FORMULA
a(n) = 2*A067411(n-2) for n>1.
G.f.: 2*z(2-11*z-2*z^2) / (1-6*z).
a(n) = 8 * 6^(n-3) for n>2.
G.f.: 9/2 - x - 1/Q(0) where Q(k)= 1 + 5^k/(1 - 2*x/(2*x + 5^k/Q(k+1) )); (continued fraction ). - Sergei N. Gladkovskii, Apr 10 2013
a(n) = 6*a(n-1) for n>2. - Colin Barker, Mar 28 2017
PROG
(PARI) Vec(2*x*(2 - 11*x - 2*x^2) / (1 - 6*x) + O(x^30)) \\ Colin Barker, Mar 28 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ralf Stephan, May 27 2003
STATUS
approved