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A130138 Triangle read by rows: T(n,k) is the number of Fibonacci binary words of length n and having k 1011's (n>=0, 0<=k<=floor((n-1)/3)). A Fibonacci binary word is a binary word having no 00 subword. 0
1, 2, 3, 5, 7, 1, 9, 4, 11, 10, 13, 20, 1, 15, 35, 5, 17, 56, 16, 19, 84, 40, 1, 21, 120, 86, 6, 23, 165, 166, 23, 25, 220, 296, 68, 1, 27, 286, 496, 171, 7, 29, 364, 791, 382, 31, 31, 455, 1211, 781, 105, 1, 33, 560, 1792, 1488, 300, 8, 35, 680, 2576, 2678, 756, 40, 37 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row n has 1+floor((n-1)/3) terms. Row sums are the Fibonacci numbers (A000045). T(n,0)=A004280(n+1). Sum(k*T(n,k), k>=0)=A004798(n-3) (n>=4).

LINKS

Table of n, a(n) for n=0..64.

FORMULA

G.f.=G(t,z)=(1+z)(1+z^3-tz^3)/[1-z-z^2+z^3-tz^3].

EXAMPLE

T(7,2)=1 because we have 1011011.

Triangle starts:

1;

2;

3;

5;

7,1;

9,4;

11,10;

13,20,1;

15,35,5;

MAPLE

G:=(1+z)*(1+z^3-t*z^3)/(1-z-z^2+z^3-t*z^3): Gser:=simplify(series(G, z=0, 24)): for n from 0 to 21 do P[n]:=sort(coeff(Gser, z, n)) od: 1; for n from 1 to 21 do seq(coeff(P[n], t, j), j=0..floor((n-1)/3)) od; # yields sequence in triangular form

CROSSREFS

Cf. A000045, A004280, A004798.

Sequence in context: A101987 A178743 A126052 * A171855 A130136 A197124

Adjacent sequences:  A130135 A130136 A130137 * A130139 A130140 A130141

KEYWORD

nonn,tabf

AUTHOR

Emeric Deutsch, May 13 2007

STATUS

approved

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Last modified February 25 13:30 EST 2018. Contains 299654 sequences. (Running on oeis4.)