A226370 Number of tilings of a 6 X n rectangle using integer-sided square tiles of area > 1.

1, 0, 1, 1, 3, 2, 7, 7, 16, 19, 40, 51, 98, 136, 245, 355, 617, 923, 1560, 2386, 3962, 6147, 10085, 15804, 25716, 40569, 65652, 104040, 167738, 266634, 428798, 683021, 1096560, 1749127, 2804915, 4478363, 7175960, 11464553, 18360713, 29346366, 46982101

Offset: 0

Author

Alois P. Heinz, Jun 05 2013

Keywords

• nonn
• easy

Examples

			a(4) = 3:
._._._._.   ._._._._.   ._._._._.
|       |   |   |   |   |   |   |
|       |   |___|___|   |___|___|
|       |   |       |   |   |   |
|_______|   |       |   |___|___|
|   |   |   |       |   |   |   |
|___|___|   |_______|   |___|___|
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,1,1,2,0,1).

Crossrefs

Column k=6 of A226206.

Programs

Maple

a:= n-> (Matrix(6, (i, j)-> `if`(i+1=j, 1,
    `if`(i=6, [1, 0, 2, 1, 1, 0][j], 0)))^n. <<1, 0, 1, 1, 3, 2>>)[1, 1]:
seq(a(n), n=0..60);

Formula

G.f.: 1/(1-x^2-x^3-2*x^4-x^6).

a(n) = a(n-2)+a(n-3)+2*a(n-4)+a(n-6) for n>5, a(0) = a(2) = a(3) = 1, a(1) = 0, a(4) = 3, a(5) = 2.