login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A219968 Number of tilings of a 3 X n rectangle using straight (3 X 1) trominoes and 2 X 2 tiles. 2
1, 1, 1, 2, 3, 4, 8, 13, 19, 35, 58, 89, 154, 256, 405, 681, 1131, 1822, 3025, 5012, 8156, 13465, 22257, 36415, 59976, 98961, 162370, 267184, 440335, 723521, 1190237, 1960146, 3223045, 5301876, 8727650, 14355677, 23615683, 38865307, 63937660, 105184761 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

FORMULA

G.f.: -(x-1)^2*(x^2+x+1)^2 / (x^9+x^7-x^6-2*x^4+3*x^3+x-1).

EXAMPLE

a(6) = 8, because there are 8 tilings of a 3 X 6 rectangle using straight (3 X 1) trominoes and 2 X 2 tiles:

._._._._._._.  ._____._._._.  ._._____._._.  ._._._____._.

| | | | | | |  |_____| | | |  | |_____| | |  | | |_____| |

| | | | | | |  |_____| | | |  | |_____| | |  | | |_____| |

|_|_|_|_|_|_|  |_____|_|_|_|  |_|_____|_|_|  |_|_|_____|_|

._._._._____.  ._____._____.  .___.___.___.  ._____._____.

| | | |_____|  |_____|_____|  |   |   |   |  |_____|_____|

| | | |_____|  |_____|_____|  |___|_._|___|  |   |   |   |

|_|_|_|_____|  |_____|_____|  |_____|_____|  |___|___|___|

MAPLE

gf:= -(x-1)^2*(x^2+x+1)^2 / (x^9+x^7-x^6-2*x^4+3*x^3+x-1):

a:= n-> coeff(series(gf, x, n+1), x, n):

seq(a(n), n=0..50);

CROSSREFS

Column k=3 of A219967.

Sequence in context: A095705 A034776 A068791 * A126042 A076227 A186272

Adjacent sequences:  A219965 A219966 A219967 * A219969 A219970 A219971

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Dec 02 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 19 06:03 EST 2019. Contains 329310 sequences. (Running on oeis4.)