A247124 Number of tilings of a 5 X n rectangle using n pentominoes of shapes I, U, X.

1, 1, 1, 2, 3, 8, 14, 21, 37, 63, 122, 221, 374, 656, 1147, 2066, 3699, 6477, 11407, 20099, 35656, 63323, 111775, 197352, 348556, 616560, 1091570, 1929721, 3410509, 6028021, 10658114, 18851012, 33331681, 58927069, 104177155, 184188343, 325686763, 575858676

Offset

0,4

Links

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

Wikipedia, Pentomino

Formula

G.f.: see Maple program.

Example

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

Maple

gf:= -(x-1)^2 *(x^4+x^3+x^2+x+1)^2 /
     (x^15 +x^13 +x^11 -3*x^10 -2*x^8 -2*x^6 +6*x^5 +x^3 +x-1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..50);

Crossrefs

Cf. A174249, A233427, A247125, A247268, A264812.

Sequence in context: A331820 A368855 A022951 * A171237 A173149 A128305

Adjacent sequences: A247121 A247122 A247123 * A247125 A247126 A247127

Keyword

nonn

Author

Alois P. Heinz, Nov 19 2014

Status

approved