A322496 Number of tilings of a 3 X n rectangle using V (2m+1)-ominoes (m >= 0) in standard orientation.

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

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: A216631 A026384 A346397 * A066143 A110045 A108931

Adjacent sequences: A322493 A322494 A322495 * A322497 A322498 A322499

Keyword

nonn,easy

Author

Alois P. Heinz, Dec 12 2018

Status

approved