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

0,3

Links

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

Formula

G.f.: see Maple program.

Example

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

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);

Crossrefs

Column k=6 of A219924.

Cf. A226549.

Sequence in context: A354670 A220711 A295915 * A228282 A303806 A304853

Adjacent sequences: A219922 A219923 A219924 * A219926 A219927 A219928

Keyword

nonn,easy

Author

Alois P. Heinz, Dec 01 2012

Status

approved