A249762 Number of tilings of a 5 X n rectangle using n pentominoes of shapes F, I, L.

1, 1, 3, 5, 13, 50, 133, 360, 875, 2254, 6336, 17331, 47199, 124476, 330344, 889454, 2400961, 6485476, 17392906, 46616158, 125153478, 336529923, 905611165, 2434088873, 6539233985, 17567977887, 47214493386, 126927551197, 341177175540, 916960655233

Offset

0,3

Links

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

Vaclav Kotesovec, G.f. and the recurrence (of order 315)

Wikipedia, Pentomino

Formula

a(n) ~ c * d^n, where d = 2.6877447474867836174937272605197376719631593933016281800670782370745298422..., c = 0.3236150736074998563483897952085529328299218049725560430481595704054051228... (1/d is the root of the denominator, see g.f.). - Vaclav Kotesovec, May 19 2015

Example

a(4) = 13:
._______.     ._______.     ._______.
| | | | |     | ._| ._|     | | ._| |
| | | | |     | |_. | |     | | | | |
| | | | |     | | |_| |     | | | | |
| | | | |     |_| ._| |     | |_| | |
|_|_|_|_| (1) |___|___| (2) |_|___|_| (2)
._______.     ._______.     ._______.
| ._| | |     | ._| ._|     | ._|_. |
| | | | |     | | | | |     | | | | |
| | | | |     | | | | |     | | | | |
|_| | | |     |_| |_| |     |_| | |_|
|___|_|_| (4) |___|___| (2) |___|___| (2) .

Crossrefs

Cf. A174249, A233427, A247443, A247680, A251617, A251737, A257866, A264765.

Sequence in context: A113606 A209002 A106879 * A264812 A276827 A034375

Adjacent sequences: A249759 A249760 A249761 * A249763 A249764 A249765

Keyword

nonn

Author

Alois P. Heinz, Dec 03 2014

Status

approved