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Search: id:A060635
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| A060635 |
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a(n) is the number of 2 X 1 domino tilings of the set S in the plane R^2 consisting of the union of the following two rectangles: rectangle1: |x| <= n, |y| <= 1, rectangle2: |x| <= 1, |y| <= n. |
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+0
1
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| 2, 8, 72, 450, 3200, 21632, 149058, 1019592, 6993800, 47922050, 328499712, 2251473408, 15432082562, 105772401800, 724976569800, 4969058770242, 34058447431808, 233440040239232, 1600021920672450, 10966713178192200
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The relevant graph has rotational symmetry so the number of tilings is a square or twice a square, in this case by the formula for a(n) it is always twice a square.
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REFERENCES
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M. Ciucu, Enumeration of perfect matchings in graphs with reflective symmetry. J. Combin. Theory Ser. A 77 (1997), no. 1, 67-97
W. Jockusch, Perfect matchings and perfect squares. J. Combin. Theory Ser. A 67 (1994), no. 1, 100-115
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,200
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FORMULA
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a(n) = 2 * F(n)^2 * F(n+1)^2 where F(n) is the n-th Fibonacci number - sequence A000045.
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EXAMPLE
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a(1) = 2 because in this case the set S is the unit square and there is one horizontal tiling and one vertical.
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MAPLE
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with(combinat): for n from 1 to 40 do printf(`%d, `, 2*fibonacci(n)^2*fibonacci(n+1)^2) od:
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PROGRAM
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(PARI) { a=1; b=0; c=1; for (n=1, 200, f=a+b; g=b+c; a=b; b=c; c=g; write("b060635.txt", n, " ", 2*f^2*g^2); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 08 2009]
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CROSSREFS
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Cf. A000045, A006253, A004003, A006125.
Sequence in context: A123117 A062733 A026739 this_sequence A009478 A038057 A005615
Adjacent sequences: A060632 A060633 A060634 this_sequence A060636 A060637 A060638
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KEYWORD
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nonn
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AUTHOR
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Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Apr 16 2001
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 16 2001
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