OFFSET
0,4
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
R. J. Mathar, Paving Rectangular Regions with Rectangular Tiles: Tatami and Non-Tatami Tilings, arXiv:1311.6135 [math.CO], 2013, Table 21.
R. J. Mathar, Tilings of Rectangular Regions by Rectangular Tiles: Counts Derived from Transfer Matrices, arXiv:1406.7788 [math.CO], 2014, eq (14).
Index entries for linear recurrences with constant coefficients, signature (1,1,7,-1,-5,-10,-1,3,5,1,-1,-1).
FORMULA
G.f.: See the definition of g in the Maple code.
MAPLE
g := (1-x^3)^2*(-x^2+1-x^3)/ (-x^10+x^12+x^11+10*x^6-5*x^9-3*x^8+x^7+x^4-7*x^3+5*x^5-x^2-x+1) ;
taylor(%, x=0, 30) ;
gfun[seriestolist](%) ;
MATHEMATICA
CoefficientList[Series[(1 - x^3)^2*(-x^2 + 1 - x^3)/(-x^10 + x^12 + x^11 + 10*x^6 - 5*x^9 - 3*x^8 + x^7 + x^4 - 7*x^3 + 5*x^5 - x^2 - x + 1), {x, 0, 50}], x] (* G. C. Greubel, Apr 27 2017 *)
PROG
(PARI) x='x+O('x^50); Vec((1-x^3)^2*(-x^2+1-x^3)/(-x^10+x^12+x^11+10*x^6 -5*x^9-3*x^8+x^7+x^4-7*x^3+5*x^5-x^2-x+1)) \\ G. C. Greubel, Apr 27 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Jan 29 2014
STATUS
approved