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

Author

Alois P. Heinz, Nov 19 2014

Keywords

• nonn

Examples

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

Links

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

Crossrefs

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

Programs

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);

Formula

G.f.: see Maple program.