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A322496 Number of tilings of a 3 X n rectangle using V (2m+1)-ominoes (m >= 0) in standard orientation. 2
1, 1, 3, 8, 18, 44, 107, 257, 621, 1500, 3620, 8740, 21101, 50941, 122983, 296908, 716798, 1730504, 4177807, 10086117, 24350041, 58786200, 141922440, 342631080, 827184601, 1997000281, 4821185163, 11639370608, 28099926378, 67839223364, 163778373107 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The shapes of the tiles are:

              ._.

       ._.    | |

  ._.  | |_.  | |_._.

  |_|  |___|  |_____|  .

LINKS

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

Wikipedia, Polyomino

Index entries for linear recurrences with constant coefficients, signature (1,2,3,1).

FORMULA

G.f.: -1/((x^2+x+1)*(x^2+2*x-1)).

a(n) = 2*a(n-1) + a(n-2) + A049347(n). - Greg Dresden, May 18 2020

EXAMPLE

a(3) = 8:

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

  |_|_|_|  | |_|_|  |_|_|_|  |_| |_|  |_|_|_|  |_| |_|  | |_|_|  | | |_|

  |_|_|_|  |___|_|  | |_|_|  |_|___|  |_| |_|  | |___|  | |_|_|  | |___|

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

MAPLE

a:= n-> (<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <1|3|2|1>>^n)[4$2]:

seq(a(n), n=0..40);

CROSSREFS

Column k=3 of A322494.

Sequence in context: A026756 A216631 A026384 * A066143 A110045 A108931

Adjacent sequences:  A322493 A322494 A322495 * A322497 A322498 A322499

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Dec 12 2018

STATUS

approved

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Last modified September 27 19:04 EDT 2020. Contains 337388 sequences. (Running on oeis4.)