A019439 Number of ways of tiling a 2 X n rectangle with dominoes and trominoes.

1, 1, 2, 6, 17, 43, 108, 280, 727, 1875, 4832, 12470, 32191, 83075, 214372, 553214, 1427673, 3684333, 9507936, 24536616, 63320419, 163407771, 421697922, 1088253936, 2808400703, 7247494517, 18703234038, 48266468208, 124558777387, 321442392689, 829529751892, 2140724511882

Offset: 0

Author

N. J. A. Sloane, Oct 04 2008

Keywords

• nonn
• easy

Comments

The old entry with this sequence number was a duplicate of A007737.

References

• Jaime Rangel-Mondragon, Polyominoes and Related Families, The Mathematica Journal, 9:3 (2005), 609-640.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2430
• Index entries for linear recurrences with constant coefficients, signature (2,0,3,2,1,-1).

Crossrefs

Column k=2 of A364457.

Programs

Maple

a:= n-> (Matrix([[1, 1, 0, 0, 1, 1]]). Matrix (6, (i,j)-> if i=j-1 then 1 elif j=1 then [2, 0, 3, 2, 1, -1][i] else 0 fi)^n)[1,2]: seq(a(n), n=0..30); # Alois P. Heinz, Sep 24 2009

Mathematica

LinearRecurrence[{2, 0, 3, 2, 1, -1}, {1, 1, 2, 6, 17, 43}, 40] // Rest (* Jean-François Alcover, Feb 18 2016 *)

Formula

G.f.: -(x^3+x-1)/(x^6-x^5-2*x^4-3*x^3-2*x+1). - Alois P. Heinz, Sep 24 2009

Extensions

More terms from Alois P. Heinz, Sep 24 2009

a(0)=1 prepended by Alois P. Heinz, Jul 25 2023