A236582 The number of tilings of an 8 X n floor with 1 X 4 tetrominoes.

1, 1, 1, 1, 7, 15, 25, 37, 100, 229, 454, 811, 1732, 3777, 7858, 15339, 31273, 65536, 136600, 276535, 562728, 1159942, 2400783, 4918159, 10052140, 20627526, 42480474, 87254743, 178855138, 366854368

Offset: 0

Author

R. J. Mathar, Jan 29 2014

Keywords

• nonn
• easy

Comments

Tilings are counted irrespective of internal symmetry: Tilings that match each other after rotations and/or reflections are counted with their multiplicity.

Links

• R. J. Mathar, Paving rectangular regions..., arXiv:1311.6135 [math.CO], 2013, Table 37.
• R. J. Mathar, Tilings of Rectangular Regions by Rectangular Tiles: Counts Derived from Transfer Matrices, arXiv:1406.7788 [math.CO], 2014, eq. (28).

Crossrefs

Cf. A003269 (4 X n floor), A236579 - A236581.

Column k=4 of A250662.

Cf. A251074.

Programs

Maple

p := (1-x)^3*(x+1)^3*(x^2+1)^3*(x^6-x^4-x^3-x^2+1) ;
q :=  -x^2 -13*x^10 -5*x^18 +8*x^6 -x -x^20 -9*x^4 +16*x^8 -13*x^12 -2*x^19 +1 +10*x^14 +5*x^7 +6*x^15 -6*x^11 +x^22 +6*x^16 +x^17 +2*x^5 -2*x^13 ;
taylor(p/q,x=0,30) ;
gfun[seriestolist](%) ;

Formula

G.f.: p(x)/q(x) with polynomials p and q defined in the Maple code.