OFFSET
0,2
COMMENTS
Tilings are counted irrespective of internal symmetry: Tilings that match each other after rotations and/or reflections are counted with their multiplicity.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Mudit Aggarwal and Samrith Ram, Generating functions for straight polyomino tilings of narrow rectangles, arXiv:2206.04437 [math.CO], 2022.
R. J. Mathar, Paving Rectangular Regions with Rectangular Tiles: Tatami and Non-Tatami Tilings, arXiv:1311.6135 [math.CO], 2013, Table 20.
R. J. Mathar, Tilings of Rectangular Regions by Rectangular Tiles: Counts Derived from Transfer Matrices, arXiv:1406.7788 [math.CO], 2014.
Index entries for linear recurrences with constant coefficients, signature (6,-3,1).
FORMULA
G.f.: (1-x)^2/(1-6*x+3*x^2-x^3).
a(n) = 6*a(n-1) - 3*a(n-2) + a(n-3). - M. Poyraz Torcuk, Oct 24 2021
MAPLE
g := (1-x)^2/(1-6*x+3*x^2-x^3) ;
taylor(%, x=0, 30) ;
gfun[seriestolist](%) ;
MATHEMATICA
CoefficientList[Series[(1 - x)^2/(1 - 6 x + 3 x^2 - x^3), {x, 0, 50}], x] (* G. C. Greubel, Apr 29 2017 *)
LinearRecurrence[{6, -3, 1}, {1, 4, 22}, 30] (* M. Poyraz Torcuk, Nov 06 2021 *)
PROG
(PARI) my(x='x+O('x^50)); Vec((1-x)^2/(1-6*x+3*x^2-x^3)) \\ G. C. Greubel, Apr 29 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Jan 29 2014
STATUS
approved