A219925 Number of tilings of a 6 X n rectangle using integer-sided square tiles.

1, 1, 13, 60, 348, 1916, 10668, 59257, 329350, 1830234, 10171315, 56525022, 314128014, 1745708992, 9701463927, 53914132251, 299618062228, 1665073290365, 9253344266757, 51423790446062, 285778433090830, 1588162056821687, 8825923956549044, 49048479247236561

Offset: 0

Author

Alois P. Heinz, Dec 01 2012

Keywords

• nonn
• easy

Examples

			a(2) = 13, because there are 13 tilings of a 6 X 2 rectangle using integer-sided square tiles:
._._.  .___.  ._._.  ._._.  ._._.  ._._.
|_|_|  |   |  |_|_|  |_|_|  |_|_|  |_|_|
|_|_|  |___|  |   |  |_|_|  |_|_|  |_|_|
|_|_|  |_|_|  |___|  |   |  |_|_|  |_|_|
|_|_|  |_|_|  |_|_|  |___|  |   |  |_|_|
|_|_|  |_|_|  |_|_|  |_|_|  |___|  |   |
|_|_|  |_|_|  |_|_|  |_|_|  |_|_|  |___|
.___.  .___.  .___.  ._._.  ._._.  ._._.  .___.
|   |  |   |  |   |  |_|_|  |_|_|  |_|_|  |   |
|___|  |___|  |___|  |   |  |   |  |_|_|  |___|
|   |  |_|_|  |_|_|  |___|  |___|  |   |  |   |
|___|  |   |  |_|_|  |   |  |_|_|  |___|  |___|
|_|_|  |___|  |   |  |___|  |   |  |   |  |   |
|_|_|  |_|_|  |___|  |_|_|  |___|  |___|  |___|
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500

Crossrefs

Column k=6 of A219924.

Cf. A226549.

Programs

Maple

gf:= -(2*x^9 +3*x^8 +2*x^7 -3*x^6 -7*x^5 -4*x^4 -3*x^3 +5*x^2 +2*x -1) / (2*x^15 +7*x^14 +12*x^13 +6*x^12 -18*x^11 -13*x^10 -8*x^9 -27*x^8 -32*x^7 +x^6 +40*x^5 +34*x^4 -3*x^3 -15*x^2 -3*x +1):
a:= n-> coeff (series (gf, x, n+1), x, n):
seq (a(n), n=0..40);

Formula

G.f.: see Maple program.