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A220129
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1 followed by period 12: (1, 5, 3, 9, 1, 7, 1, 9, 3, 5, 1, 11) repeated; offset 0.
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2
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1, 1, 5, 3, 9, 1, 7, 1, 9, 3, 5, 1, 11, 1, 5, 3, 9, 1, 7, 1, 9, 3, 5, 1, 11, 1, 5, 3, 9, 1, 7, 1, 9, 3, 5, 1, 11, 1, 5, 3, 9, 1, 7, 1, 9, 3, 5, 1, 11, 1, 5, 3, 9, 1, 7, 1, 9, 3, 5, 1, 11, 1, 5, 3, 9, 1, 7, 1, 9, 3, 5, 1, 11, 1, 5, 3, 9, 1, 7, 1, 9, 3, 5, 1, 11
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OFFSET
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0,3
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COMMENTS
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Also the number of tilings of an n X 4 rectangle using integer-sided rectangular tiles of area n.
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LINKS
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FORMULA
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G.f.: -(10*x^6+11*x^5+16*x^4+9*x^3+7*x^2+2*x+1) / (x^6+x^5+x^4-x^2-x-1).
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EXAMPLE
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a(6) = 7, because there are 7 tilings of a 6 X 4 rectangle using integer-sided rectangular tiles of area 6:
._._._._. ._._._._. ._._____. .___._._.
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| | | | | |_____| | | |_____| | | | |
| | | | | | | | | | | |___| | |
| | | | | |_____| | | |_____| | | | |
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|_|_|_|_| |_____|_| |_|_____| |___|_|_|
._.___._. ._._.___. .___.___.
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| |___| | | | |___| |___|___|
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|_|___|_| |_|_|___| |___|___|
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MAPLE
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a:= n-> `if`(n=0, 1, [11, 1, 5, 3, 9, 1, 7, 1, 9, 3, 5, 1][irem(n, 12)+1]):
seq(a(n), n=0..100);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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