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A134438 Number of tilings of a 3 X n rectangle with n trominoes. 13
1, 1, 3, 10, 23, 62, 170, 441, 1173, 3127, 8266, 21937, 58234, 154390, 409573, 1086567, 2882021, 7645046, 20279829, 53794224, 142696606, 378522507, 1004078871, 2663452699, 7065162260, 18741269167, 49713692146, 131872134232, 349808216915, 927912454723 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
REFERENCES
G. Kreweras, Recouvrements d'un rectangle de largeur 3 à l'aide de triminos, Mathématiques et sciences humaines, tome 130 (1995), p. 27-31.
LINKS
Wikipedia, Tromino
FORMULA
a(n) = a(n-1) +2*a(n-2) +6*a(n-3) +a(n-4) -a(n-6).
G.f.: (1-x^3) / (1-x-2*x^2-6*x^3-x^4+x^6). - Alois P. Heinz, Oct 09 2008
MAPLE
a:= n-> (Matrix([[1$2, 0$2, 1, 0]]). Matrix(6, (i, j)-> if i+1=j then 1 elif j=1 then [1, 2, 6, 1, 0, -1][i] else 0 fi)^n)[1, 2]: seq(a(n), n=0..30); # Alois P. Heinz, Oct 09 2008
MATHEMATICA
LinearRecurrence[{1, 2, 6, 1, 0, -1}, {1, 1, 3, 10, 23, 62}, 40] (* Harvey P. Dale, Aug 27 2013 *)
CROSSREFS
Column k=3 of A233320.
Sequence in context: A167243 A316403 A185828 * A092255 A105861 A228493
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Jan 18 2008
EXTENSIONS
More terms from Alois P. Heinz, Oct 09 2008
STATUS
approved

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Last modified February 21 01:21 EST 2024. Contains 370219 sequences. (Running on oeis4.)