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

Offset

0,3

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).

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

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 *)

Crossrefs

Column k=2 of A364457.

Sequence in context: A229732 A130104 A014833 * A018024 A364450 A190159

Adjacent sequences: A019436 A019437 A019438 * A019440 A019441 A019442

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 04 2008

Extensions

More terms from Alois P. Heinz, Sep 24 2009

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

Status

approved