login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A270062 Number of tilings of a 2 X n rectangle using monominoes and trominoes of any shape. 2
1, 1, 5, 14, 45, 140, 438, 1371, 4287, 13413, 41956, 131249, 410572, 1284352, 4017713, 12568213, 39315905, 122988066, 384731445, 1203517448, 3764844982, 11777193395, 36841433019, 115247422841, 360517151000, 1127770261265, 3527892525112, 11035958382864 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

Wikipedia, Tromino

Index entries for linear recurrences with constant coefficients, signature (1,5,5,1,-1,-1).

FORMULA

G.f.: -(x^3+x^2-1)/(x^6+x^5-x^4-5*x^3-5*x^2-x+1).

a(n) = a(n-1) +5*(a(n-2)+a(n-3)) +a(n-4) -a(n-5) -a(n-6).

EXAMPLE

a(3) = 14:

._____.  ._____.  ._____.  ._____.  ._____.  ._____.  ._____.

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

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

.

._____.  ._____.  ._____.  ._____.  ._____.  ._____.  ._____.

|_|_|_|  | ._| |  | |_. |  |_|_| |  |_| |_|  |_| ._|  |_|_. |

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

.

MAPLE

a:= n-> (Matrix(6, (i, j)-> `if`(i+1=j, 1, `if`(i=6, [-1$2, 1,

         5$2, 1][j], 0)))^n. <<1, 1, 5, 14, 45, 140>>)[1, 1]:

seq(a(n), n=0..30);

CROSSREFS

Column k=2 of A270061.

Sequence in context: A140796 A197212 A100059 * A236043 A270661 A222908

Adjacent sequences:  A270059 A270060 A270061 * A270063 A270064 A270065

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Mar 09 2016

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 January 22 07:39 EST 2020. Contains 331139 sequences. (Running on oeis4.)