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A034999
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Number of ways to cut a 2 X n rectangle into rectangles with integer sides.
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6
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1, 2, 8, 34, 148, 650, 2864, 12634, 55756, 246098, 1086296, 4795090, 21166468, 93433178, 412433792, 1820570506, 8036386492, 35474325410, 156591247016, 691227204226, 3051224496244, 13468756547882, 59453967813584, 262442511046330, 1158477291582892
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OFFSET
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0,2
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COMMENTS
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Hankel transform is 1, 4, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... . - Philippe Deléham, Dec 10 2011
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LINKS
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Table of n, a(n) for n=0..24.
David A. Klarner and Spyros S. Magliveras, The number of tilings of a block with blocks, European Journal of Combinatorics 9 (1988), 317-330.
Index entries for linear recurrences with constant coefficients, signature (6,-7).
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FORMULA
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a(n) = 1+3^(n-1) + Sum_{i=1..n-1} (1+3^(i-1)) a(n-i).
a(n) = 6a(n - 1) - 7a(n - 2), a(n) = ((4 + sqrt(2)) (3 + sqrt(2))^n + (4 - sqrt(2)) (3 - sqrt(2))^n)/14. - N. Sato, May 10 2006
G.f.: (1-x)*(1-3*x)/(1-6*x+7*x^2). - Richard Stanley, Dec 09 2011
E.g.f.: (3 + exp(3*x)*(4*cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x)))/7. - Stefano Spezia, Feb 17 2022
a(n) = 2*A086351(n-1), n>0. - R. J. Mathar, Apr 07 2022
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EXAMPLE
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For n=2 the a(2) = 8 ways to cut are:
.___. .___. .___. .___. .___. .___. .___. .___.
| | | | | |___| | |_| |_| | |___| |_|_| |_|_|
|___| |_|_| |___| |_|_| |_|_| |_|_| |___| |_|_| .
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CROSSREFS
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Column 2 of A116694. - Alois P. Heinz, Dec 10 2012
Sequence in context: A014445 A113440 A296227 * A067336 A245090 A151829
Adjacent sequences: A034996 A034997 A034998 * A035000 A035001 A035002
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KEYWORD
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nonn,easy
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AUTHOR
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Erich Friedman
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EXTENSIONS
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a(0) added by Richard Stanley, Dec 09 2011
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STATUS
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approved
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