%I A129709
%S A129709 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,
%T A129709 108,18,13,125,188,50,1,14,161,308,121,6,15,203,483,261,25,16,252,728,
%U A129709 520,80,1,17,308,1064,968,220,7,18,372,1512,1710,536,33,19,444,2100
%N 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.
%C A129709 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).
%F A129709 G.f.=G(t,z)=(1+z)/(1-z-z^2+z^3-tz^3).
%e A129709 T(7,2)=4 because we have 1011011,0111011,0110110 and 0110111.
%e A129709 Triangle starts:
%e A129709 1;
%e A129709 2;
%e A129709 3;
%e A129709 4,1;
%e A129709 5,3;
%e A129709 6,7;
%e A129709 7,13,1;
%e A129709 8,22,4;
%e A129709 9,34,12;
%e A129709 10,50,28,1;
%p A129709 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
%Y A129709 Cf. A000045, A023610.
%Y A129709 Sequence in context: A026280 A115994 A071437 this_sequence A133108 A055441 
               A104717
%Y A129709 Adjacent sequences: A129706 A129707 A129708 this_sequence A129710 A129711 
               A129712
%K A129709 nonn,tabf
%O A129709 0,2
%A A129709 Emeric Deutsch (deutsch(AT)duke.poly.edu), May 12 2007