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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
Wikipedia, Polyomino
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
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Dec 12 2018
STATUS
approved

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Last modified April 23 10:07 EDT 2024. Contains 371905 sequences. (Running on oeis4.)