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