A234931 Number of tilings of a 5 X n rectangle using n pentominoes of shapes F, U, N.

1, 0, 0, 0, 2, 0, 0, 0, 4, 0, 8, 0, 16, 0, 40, 0, 64, 16, 200, 96, 504, 464, 1528, 1664, 4376, 5616, 12792, 18192, 38264, 58384, 115832, 186368, 355808, 589344, 1095408, 1853664, 3383656, 5802016, 10470376, 18125280, 32461312, 56552736, 100782696, 176318464

Offset

0,5

Links

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

Wikipedia, Pentomino

Formula

G.f.: (4*x^20 +4*x^18 +8*x^16 -3*x^14 +4*x^13 -5*x^12 -2*x^11 +3*x^10 -2*x^9 +6*x^8 -2*x^7 +2*x^6 -2*x^5 -x^4 +2*x -1) / (-8*x^22 -28*x^20 -6*x^18 +8*x^17 +26*x^16 +4*x^15 +7*x^14 -8*x^13 -9*x^12 -14*x^11 +7*x^10 +2*x^9 +8*x^8 -2*x^7 +2*x^6 -6*x^5 +x^4 +2*x -1).

Example

a(4) = 2:
._______.   ._______.
| | ._. |   | ._. | |
| |_| |_|   |_| |_| |
|_. |_. |   | ._| ._|
| |_| | |   | | |_| |
|_____|_|   |_|_____|.

Crossrefs

Cf. A174249, A233427, A234312, A247680, A247126.

Sequence in context: A285182 A190608 A011991 * A129183 A280292 A181566

Adjacent sequences: A234928 A234929 A234930 * A234932 A234933 A234934

Keyword

nonn

Author

Alois P. Heinz, Jan 01 2014

Status

approved