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

Author

Alois P. Heinz, Dec 12 2018

Keywords

• nonn
• easy

Comments

The shapes of the tiles are:

._.

._. | |

.. | |. | |..

|| |__| |___| .

Examples

			a(3) = 8:
  ._____.  ._____.  ._____.  ._____.  ._____.  ._____.  ._____.  ._____.
  |_|_|_|  | |_|_|  |_|_|_|  |_| |_|  |_|_|_|  |_| |_|  | |_|_|  | | |_|
  |_|_|_|  |___|_|  | |_|_|  |_|___|  |_| |_|  | |___|  | |_|_|  | |___|
  |_|_|_|  |_|_|_|  |___|_|  |_|_|_|  |_|___|  |___|_|  |_____|  |_____|  .
		

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).

Crossrefs

Column k=3 of A322494.

Programs

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);

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