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

Author

R. J. Mathar, Jan 29 2014

Keywords

• easy
• 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..., 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).

Crossrefs

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

Programs

Maple

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

Formula

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