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A129709 Triangle read by rows: T(n,k) is the number of Fibonacci binary words of length n and having k 011 subwords (0<=k<=floor(n/3)). A Fibonacci binary word is a binary word having no 00 subword. 0
1, 2, 3, 4, 1, 5, 3, 6, 7, 7, 13, 1, 8, 22, 4, 9, 34, 12, 10, 50, 28, 1, 11, 70, 58, 5, 12, 95, 108, 18, 13, 125, 188, 50, 1, 14, 161, 308, 121, 6, 15, 203, 483, 261, 25, 16, 252, 728, 520, 80, 1, 17, 308, 1064, 968, 220, 7, 18, 372, 1512, 1710, 536, 33, 19, 444, 2100 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also number of Fibonacci binary words of length n and having k 110 subwords. Row n has 1+floor(n/3) terms. Row sums are the Fibonacci numbers (A000045). T(n,0)=n+1. Sum(k*T(n,k), k>=0)=A023610(n-3).

LINKS

Table of n, a(n) for n=0..65.

FORMULA

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

EXAMPLE

T(7,2)=4 because we have 1011011,0111011,0110110 and 0110111.

Triangle starts:

1;

2;

3;

4,1;

5,3;

6,7;

7,13,1;

8,22,4;

9,34,12;

10,50,28,1;

MAPLE

G:=(1+z)/(1-z-z^2+z^3-t*z^3): Gser:=simplify(series(G, z=0, 23)): for n from 0 to 20 do P[n]:=sort(coeff(Gser, z, n)) od: for n from 0 to 20 do seq(coeff(P[n], t, j), j=0..floor(n/3)) od; # yields sequence in triangular form

CROSSREFS

Cf. A000045, A023610.

Sequence in context: A071437 A243713 A332266 * A253146 A253028 A133108

Adjacent sequences:  A129706 A129707 A129708 * A129710 A129711 A129712

KEYWORD

nonn,tabf

AUTHOR

Emeric Deutsch, May 12 2007

STATUS

approved

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Last modified October 25 14:34 EDT 2021. Contains 348255 sequences. (Running on oeis4.)