A220769 Number of tilings of a 3 X n rectangle using integer-sided rectangular tiles of equal area.

1, 2, 6, 4, 20, 7, 54, 12, 190, 23, 616, 44, 2266, 91, 8136, 198, 30214, 409, 111540, 875, 415601, 1887, 1546170, 4026, 5767198, 8649, 21503856, 18583, 80237366, 39868, 299369546, 85629, 1117185300, 183962, 4169054092, 395051, 15558753295, 848494, 58064626980

Offset

0,2

Comments

a(n)^(1/n) tends to sqrt(2+sqrt(3)) = 1.93185165257813657349... if n is even and to r = (1 + ((29 - 3*sqrt(93))/2)^(1/3) + ((29 + 3*sqrt(93))/2)^(1/3))/3 = 1.46557123187676802665... (where r is the real root of the equation r^2*(r-1) = 1) if n is odd. - Vaclav Kotesovec, Sep 07 2016

Links

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

Example

a(5) = 7:
._________.  ._________.  ._________.  ._________.
|         |  |_________|  | | | | | |  |_____| | |
|         |  |_________|  | | | | | |  |_____| | |
|_________|  |_________|  |_|_|_|_|_|  |_____|_|_|
._________.  ._________.  ._________.
| |_____| |  | | |_____|  |_|_|_|_|_|
| |_____| |  | | |_____|  |_|_|_|_|_|
|_|_____|_|  |_|_|_____|  |_|_|_|_|_|

Crossrefs

Column k=3 of A220777.

Sequence in context: A009262 A127699 A100140 * A124838 A247578 A088659

Adjacent sequences: A220766 A220767 A220768 * A220770 A220771 A220772

Keyword

nonn

Author

Alois P. Heinz, Dec 19 2012

Status

approved