A236581 The number of tilings of a 7 X (4n) floor with 1 X 4 tetrominoes.

1, 5, 37, 269, 1949, 14121, 102313, 741305, 5371097, 38916077, 281964941, 2042966149, 14802232757, 107249008849, 777068573905, 5630220503025, 40793546383409, 295568073335893, 2141527121824885, 15516352499614333, 112423136012925517, 814557513519681785

Offset: 0

Author

R. J. Mathar, Jan 29 2014

Keywords

• nonn

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).

Crossrefs

Cf. A003269 (4Xn floor), A236579 - A236582.

Programs

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 *)

Formula

G.f.: (1-x)^3/(-8*x+1+6*x^2-4*x^3+x^4).