A134438 Number of tilings of a 3 X n rectangle with n trominoes.

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

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

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Wikipedia, Tromino

Index entries for linear recurrences with constant coefficients, signature (1,2,6,1,0,-1).

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

Cf. A174248, A174249, A174250, A174251, A174252, A174253, A215826, A233290, A269664, A270063.

Column k=3 of A233320.

Sequence in context: A167243 A316403 A185828 * A092255 A105861 A228493

Adjacent sequences: A134435 A134436 A134437 * A134439 A134440 A134441

Keyword

nonn,easy

Author

Philippe Deléham, Jan 18 2008

Extensions

More terms from Alois P. Heinz, Oct 09 2008

Status

approved