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Search: id:A130137
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| A130137 |
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Number of Fibonacci binary words of length n having no 0110 subword. A Fibonacci binary word is a binary word having no 00 subword. |
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+0
2
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| 1, 2, 3, 5, 7, 11, 16, 25, 37, 57, 85, 130, 195, 297, 447, 679, 1024, 1553, 2345, 3553, 5369, 8130, 12291, 18605, 28135, 42579, 64400, 97449, 147405, 223033, 337389, 510466, 772227, 1168337, 1767487, 2674063, 4045440, 6120353, 9259217, 14008193
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n)=A130136(n,0).
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FORMULA
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G.f.=(1+z+z^3)/(1-z-z^2+z^3-z^4). Rec. rel.: a(n)=a(n-1)+a(n-2)-a(n-3)+a(n-4); a(0)=1, a(1)=2, a(2)=3, a(3)=5.
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EXAMPLE
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a(4)=7 because from the 8 Fibonacci binary words of length 4 only 0110 does not qualify.
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MAPLE
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a[0]:=1: a[1]:=2: a[2]:=3: a[3]:=5: for n from 4 to 45 do a[n]:=a[n-1]+a[n-2]-a[n-3]+a[n-4] od: seq(a[n], n=0..45);
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CROSSREFS
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Cf. A130136.
Sequence in context: A112088 A117792 A018057 this_sequence A091980 A005685 A092180
Adjacent sequences: A130134 A130135 A130136 this_sequence A130138 A130139 A130140
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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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