%I A118897
%S A118897 1,2,4,8,15,1,29,2,1,56,5,2,1,108,12,5,2,1,208,28,12,5,2,1,401,62,29,12,
%T A118897 5,2,1,773,136,65,30,12,5,2,1,1490,294,145,68,31,12,5,2,1,2872,628,319,
%U A118897 154,71,32,12,5,2,1,5536,1328,694,344,163,74,33,12,5,2,1,10671,2787
%N A118897 Triangle read by rows: T(n,k) is the number of binary sequences of length 
               n containing k subsequences 0000 (n,k>=0).
%C A118897 Row n has n-2 terms (n>=3). Sum of entries in row n is 2^n (A000079). 
               T(n,0)=A000078(n+4) (tetranacci numbers). T(n,1)=A118898(n). Sum(k*T(n,
               k),n>=0)=(n-3)*2^(n-4) (A001787).
%F A118897 G.f.=G(t,z)=[1+(1-t)(z+z^2+z^3)]/[1-(1+t)z-(1-t)(z^2+z^3+z^4)].
%e A118897 T(7,2)=5 because we have 0000010,0000011,0100000,1100000 and 1000001.
%e A118897 Triangle starts:
%e A118897 1;
%e A118897 2;
%e A118897 4;
%e A118897 8;
%e A118897 15,1;
%e A118897 29,2,1;
%e A118897 56,5,2,1;
%e A118897 108,12,5,2,1;
%p A118897 G:=(1+(1-t)*(z+z^2+z^3))/(1-(1+t)*z-(1-t)*(z^2+z^3+z^4)): Gser:=simplify(series(G,
               z=0,17)): P[0]:=1: for n from 1 to 14 do P[n]:=sort(coeff(Gser,z^n)) 
               od: 1;2;4;8; for n from 4 to 14 do seq(coeff(P[n],t,j),j=0..n-3) 
               od; # yields sequence in triangular form
%Y A118897 Cf. A000079, A000078, A118898, A011787.
%Y A118897 Sequence in context: A118884 A118890 A118869 this_sequence A098056 A097100 
               A002954
%Y A118897 Adjacent sequences: A118894 A118895 A118896 this_sequence A118898 A118899 
               A118900
%K A118897 nonn,tabf
%O A118897 0,2
%A A118897 Emeric Deutsch (deutsch(AT)duke.poly.edu), May 04 2006