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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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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Hankel transform is : 1, 4, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...- DELEHAM Philippe, Dec 10 2011
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (6,-7).
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FORMULA
| 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 (nsato7(AT)yahoo.ca), May 10 2006
G.f.: (1-x)*(1-3*x)/(1-6*x+7*x^2). - Richard Stanley, Dec 09 2011
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EXAMPLE
| For a 2 X 2 rectangle we have: 11 11 12 11 12 21 23 12 11 22 12 23 13 31 11 23
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CROSSREFS
| Sequence in context: A192402 A014445 A113440 * A067336 A151829 A026387
Adjacent sequences: A034996 A034997 A034998 * A035000 A035001 A035002
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KEYWORD
| nonn
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AUTHOR
| Erich Friedman (erich.friedman(AT)stetson.edu)
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EXTENSIONS
| a(0) added by Richard Stanley, Dec 09 2011
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