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Search: id:A061667
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| A061667 |
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a(n) = Fibonacci(2n+1)-2^(n-1); g.f.: (1-2x+x^2)/((1-2x)(1-3x+x^2)). |
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12
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| 1, 3, 9, 26, 73, 201, 546, 1469, 3925, 10434, 27633, 72977, 192322, 506037, 1329885, 3491810, 9161929, 24026745, 62983842, 165055853, 432445861, 1132806018, 2967020769, 7770353441, 20348233858, 53282736741, 139516753581
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Number of cells in the bottom row of all directed column-convex polyominoes of area n+1.
Also the binomial transform of A000071 (after removing its 2 leading zeros). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 04 2008]
Equals row sums of triangle A147293 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 05 2008]
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REFERENCES
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E. Barcucci, R. Pinzani and R. Sprugnoli, Directed column-convex polyominoes by recurrence relations, Lecture Notes in Computer Science, No. 668, Springer, Berlin, 1993, pp. 282-298.
A. Burstein and T. Mansour, Words restricted by 3-letter ..., Annals. Combin., 7 (2003), 1-14; see Th. 3.8.
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LINKS
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A. Burstein and T. Mansour, Words restricted by 3-letter ....
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FORMULA
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a(n)=sum{k=0..n+1, C(n+1, k)*sum{j=0..floor(k/2), Fibonacci(k-2j)}} - Paul Barry (pbarry(AT)wit.ie), Apr 17 2005
a(n) = 2*A001906(n+1)-A001906(n)-A000079(n). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 16 2007
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CROSSREFS
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Cf. A147293 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 05 2008]
Sequence in context: A084787 A121190 A054447 this_sequence A127911 A116423 A077845
Adjacent sequences: A061664 A061665 A061666 this_sequence A061668 A061669 A061670
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KEYWORD
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nonn,new
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 16 2001
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