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A220769 Number of tilings of a 3 X n rectangle using integer sided rectangular tiles of equal area. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A174824 A009262 A127699 * A124838 A247578 A088659

Adjacent sequences:  A220766 A220767 A220768 * A220770 A220771 A220772

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Dec 19 2012

STATUS

approved

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Last modified August 4 16:59 EDT 2021. Contains 346454 sequences. (Running on oeis4.)