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A347636
Number of ways to tile an n X n square with 1 X 1 squares and (n-2) X 2 vertical or horizontal rectangles.
0
193, 399, 783, 1601, 3283, 6947, 14897, 32607, 72175, 161649, 364611, 827555, 1885729, 4310639, 9874319, 22654881, 52032883, 119601123, 275058321, 632823743, 1456319215, 3352072913, 7716633443, 17765737443, 40904125825, 94182711375
OFFSET
5,1
FORMULA
a(n) = 2*A006130(n) + 12*F(n + 1) + 16*F(n - 1) - 31 for F(n) = A000045(n) the Fibonacci sequence.
a(n) = 3*a(n-1) + a(n-2) - 7*a(n-3) + a(n-4) + 3*a(n-5).
EXAMPLE
Here are two of the 193 possible tilings for a 5 X 5 square (using 1 X 1 squares and 3 X 2 rectangles):
._________ ._________
|_| |_| |_|_| |
|_|_ _ _|_| | |_ _ _|
| |_| | | |_| |
| |_| | |___|_| |
|___|_|___| |_|_|_|___|
CROSSREFS
Cf. A335560 which is the same problem but with 1 X 1 squares and (n-1) X 1 rectangles, and A337024 which uses 1 X 1 squares and 2 X 2 squares.
Sequence in context: A100363 A142500 A328137 * A113000 A105129 A140631
KEYWORD
nonn,easy
AUTHOR
STATUS
approved