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
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 36.
R. J. Mathar, Tilings of Rectangular Regions by Rectangular Tiles: Counts Derived from Transfer Matrices, arXiv:1406.7788 [math.CO], eq. (27).
Index entries for linear recurrences with constant coefficients, signature (8,-6,4,-1).
FORMULA
G.f.: (1-x)^3/(-8*x+1+6*x^2-4*x^3+x^4).
MAPLE
g := (1-x)^3/(-8*x+1+6*x^2-4*x^3+x^4) ;
taylor(%, x=0, 30) ;
gfun[seriestolist](%) ;
MATHEMATICA
LinearRecurrence[{8, -6, 4, -1}, {1, 5, 37, 269}, 19] (* Jean-François Alcover, Feb 19 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
R. J. Mathar, Jan 29 2014
STATUS
approved