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A236576
The number of tilings of a 5 X (3n) floor with 1 X 3 trominoes.
5
1, 4, 22, 121, 664, 3643, 19987, 109657, 601624, 3300760, 18109345, 99355414, 545105209, 2990674357, 16408085929, 90021597712, 493896002842, 2709719309845, 14866649448256, 81564634762843, 447497579542135
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.
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
Cf. A000930 (3 X n floor), A049086 (4 X 3n floor), A236577, A236578.
Sequence in context: A025569 A098834 A065983 * A375724 A185858 A180034
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Jan 29 2014
STATUS
approved