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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
OFFSET
0,3
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
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Mar 09 2016
STATUS
approved