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Search: id:A129715
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| A129715 |
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Number of runs in all Fibonacci binary words of length n. A Fibonacci binary word is a binary word having no 00 subword. A run is a maximal sequence of consecutive identical letters. |
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+0
2
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| 0, 2, 5, 11, 22, 43, 81, 150, 273, 491, 874, 1543, 2705, 4714, 8173, 14107, 24254, 41555, 70977, 120894, 205401, 348187, 589010, 994511, 1676257, 2820818, 4739861, 7953515, 13328998, 22310971, 37304049, 62307558, 103968225, 173324939
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OFFSET
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0,2
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COMMENT
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a(n)=Sum(k*A129714(n,k),k=0..n).
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FORMULA
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G.f.=z(2+z-z^2-z^3)/(1-z-z^2)^2. Rec. rel.: a(n)=a(n-1)+a(n-2)+2F(n) for n>=3, where F(n) is a Fibonacci number (F(0)=0,F(1)=1).
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EXAMPLE
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a(3)=11 because in the Fibonacci binary words 011, 111, 101, 010, and 110 we have a total of 2+1+3+3+2=11 runs.
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MAPLE
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with(combinat): a[0]:=0: a[1]:=2: a[2]:=5: for n from 3 to 40 do a[n]:=a[n-1]+a[n-2]+2*fibonacci(n) od: seq(a[n], n=0..40);
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CROSSREFS
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Cf. A129714.
Sequence in context: A058696 A134508 A091357 this_sequence A024493 A130781 A071015
Adjacent sequences: A129712 A129713 A129714 this_sequence A129716 A129717 A129718
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), May 12 2007
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