A248102 Number of tilings of a 5 X 2n rectangle using 2n pentominoes of shapes N, Y.

1, 0, 0, 18, 24, 238, 842, 4360, 25900, 112178, 613140, 2941170, 14789274, 74895336, 369603312, 1866863986, 9294391952, 46543456838, 233028690018, 1164275409976, 5830080180396, 29149585256266, 145845002931724, 729627382873090, 3649578988919810

Offset: 0

Author

Alois P. Heinz, Oct 01 2014

Keywords

• nonn

Examples

			a(3) = 18:
._______._._.        .___._______.        .___._______.
|_. .___| | |        |_. |___. ._|        |_. |___. ._|
| |_| | ._| |        | |_____|_| |        | |_____|_| |
| ._| | |_. |        | |___. ._| |        | |___. |_. |
| | ._|_| |_|        | ._| |_|_. |        | ._| |___| |
|_|_|_______| (*2)   |_|_______|_| (*8)   |_|_______|_| (*8)  .
		

Links

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

Crossrefs

Cf. A174249, A233427, A234312, A234931, A247680, A247443.

Formula

G.f.: (8*x^15 -52*x^14 -64*x^13 +1087*x^12 -2822*x^11 +2369*x^10 +810*x^9 -2047*x^8 +300*x^7 +122*x^6 +208*x^5 +x^4 +6*x^3 +9*x^2 +2*x -1) / (24*x^15 +4*x^14 -680*x^13 +2673*x^12 -4212*x^11 +2139*x^10 +1574*x^9 -2141*x^8 +456*x^7 -160*x^6 +236*x^5 -11*x^4 +24*x^3 +9*x^2 +2*x -1).