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

0,4

Links

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

Wikipedia, Pentomino

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).

Example

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

Crossrefs

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

Sequence in context: A364998 A369540 A125261 * A166646 A109144 A166471

Adjacent sequences: A248099 A248100 A248101 * A248103 A248104 A248105

Keyword

nonn

Author

Alois P. Heinz, Oct 01 2014

Status

approved