A236580 The number of tilings of a 6 X (4n) floor with 1 X 4 tetrominoes.

1, 4, 25, 154, 943, 5773, 35344, 216388, 1324801, 8110882, 49657576, 304020556, 1861317163, 11395616227, 69767835259, 427142397547, 2615110919020, 16010597772667, 98022320649478, 600125959188877, 3674175070596919, 22494548423870416, 137719270059617428

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

Table of n, a(n) for n=0..22.

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..., arXiv:1311.6135, Table 35.

R. J. Mathar, Tilings of Rectangular Regions by Rectangular Tiles: Counts Derived from Transfer Matrices, arXiv:1406.7788 [math.CO], eq. (26).

Index entries for linear recurrences with constant coefficients, signature (7,-6,4,-1).

Formula

G.f.: (1-x)^3/(-7*x+1+6*x^2-4*x^3+x^4).

Maple

g := (1-x)^3/(-7*x+1+6*x^2-4*x^3+x^4) ;
taylor(%, x=0, 30) ;
gfun[seriestolist](%) ;

Crossrefs

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

Sequence in context: A221849 A055846 A091634 * A010909 A079750 A195510

Adjacent sequences: A236577 A236578 A236579 * A236581 A236582 A236583

Keyword

easy,nonn

Author

R. J. Mathar, Jan 29 2014

Status

approved