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A234833
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Number of tilings of a box with sides 2 X 2 X 3n in R^3 by boxes of sides Tricube-V(3-dimensional dominoes).
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0
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1, 44, 2800, 181952, 11835136, 769854464, 50077757440, 3257475448832, 211893401092096, 13783315988086784, 896581954180218880, 58321176214542221312, 3793696247386269024256, 246773678989074187157504
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OFFSET
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0,2
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COMMENTS
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a(n): Number of tilings of a box with sides 2 X 2 X 3n in R^3 by boxes of sides Tricube-V(3-dimensional dominoes).
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LINKS
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FORMULA
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a(n) = 68*a(n-1) - 192*a(n-2).
a(n) = (2^(n-1)/C)*((-5+C)*(17-C)^n+(5+C)*(17+C)^n), where C = sqrt(241). - L. Edson Jeffery, Dec 31 2013
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EXAMPLE
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With the 16 tricube-V blocks in R^3 how many dfferent types of 2 X 2 X 12 sized volumetric regions can be attained?
For a(1)=44 and a(2)=2800, a(3)=68*a(2)-192*a(1)=68*2800-192*44=181952.
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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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EXTENSIONS
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STATUS
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approved
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