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A130137 Number of Fibonacci binary words of length n having no 0110 subword. A Fibonacci binary word is a binary word having no 00 subword. 2
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; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n)=A130136(n,0).

LINKS

Table of n, a(n) for n=0..39.

FORMULA

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.

EXAMPLE

a(4)=7 because from the 8 Fibonacci binary words of length 4 only 0110 does not qualify.

MAPLE

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);

CROSSREFS

Cf. A130136.

Sequence in context: A154888 A271485 A018057 * A218022 A091980 A274113

Adjacent sequences:  A130134 A130135 A130136 * A130138 A130139 A130140

KEYWORD

nonn

AUTHOR

Emeric Deutsch, May 13 2007

STATUS

approved

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Last modified February 21 15:58 EST 2018. Contains 299414 sequences. (Running on oeis4.)