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Search: id:A129722
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| A129722 |
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Number of 0's in even position in all Fibonacci binary words of length n. A Fibonacci binary word is a binary word having no 00 subword. |
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+0
3
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| 0, 0, 1, 1, 5, 6, 19, 25, 65, 90, 210, 300, 654, 954, 1985, 2939, 5911, 8850, 17345, 26195, 50305, 76500, 144516, 221016, 411900, 632916, 1166209, 1799125, 3283145, 5082270, 9197455, 14279725, 25655489, 39935214, 71293590, 111228804
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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a(2n+1)=a(2n)+a(2n-1) (n>=1). a(2n+1)=A001871(n-1) (n>=1). a(2n)=A129720(2n)=A001870(n-1). a(n)=Sum(k*A129721(n,k), k=0..floor(n/2)).
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FORMULA
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G.f.=z^2/[(1+z-z^2)(1-z-z^2)^2].
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EXAMPLE
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a(4)=5 because in 1110', 1111, 1101, 10'10', 10'11, 0110', 0111, and 0101 one has altogether five 0's in even position (marked by ').
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MAPLE
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G:=z^2/(1-z-z^2)^2/(1+z-z^2): Gser:=series(G, z=0, 45): seq(coeff(Gser, z, n), n=0..42);
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CROSSREFS
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Cf. A001870, A001871, A129719, A129720, A129721.
Sequence in context: A063445 A031448 A056509 this_sequence A133608 A072577 A057520
Adjacent sequences: A129719 A129720 A129721 this_sequence A129723 A129724 A129725
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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 13 2007
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