%I A118890
%S A118890 1,2,4,8,15,1,28,4,52,12,97,30,1,181,70,5,338,156,18,631,339,53,1,1178,
%T A118890 722,142,6,2199,1515,357,25,4105,3140,862,84,1,7663,6444,2018,252,7,
%U A118890 14305,13116,4614,700,33,26704,26513,10348,1846,124,1,49850,53280,22844
%N A118890 Triangle read by rows: T(n,k) is the number of binary sequences of length 
               n containing k subsequences 0110 (n,k>=0).
%C A118890 Row n has ceil(n/3) terms (n>=1). Sum of entries in row n is 2^n (A000079). 
               T(n,0)=A049864(n). T(n,1)=A118892(n). Sum(k*T(n,k),n>=0)=(n-3)*2^(n-4) 
               (A001787).
%F A118890 G.f.=G(t,z)=[1+(1-t)z^3]/[1-2z+(1-t)(1-z)z^3].
%e A118890 T(8,2)=5 because we have 01100110,01101100,01101101,00110110 and 10110110.
%e A118890 Triangle starts:
%e A118890 1;
%e A118890 2;
%e A118890 4;
%e A118890 8;
%e A118890 15,1;
%e A118890 28,4;
%e A118890 52,12;
%e A118890 97,30,1;
%p A118890 G:=(1+(1-t)*z^3)/(1-2*z+(1-t)*(1-z)*z^3): Gser:=simplify(series(G,z=0,
               24)): P[0]:=1: for n from 1 to 18 do P[n]:=sort(coeff(Gser,z^n)) 
               od: 1; for n from 1 to 18 do seq(coeff(P[n],t,j),j=0..ceil(n/3)-1) 
               od; # yields sequence in triangular form
%Y A118890 Cf. A000079, A049864, A118892, A011787.
%Y A118890 Sequence in context: A028398 A155249 A118884 this_sequence A118869 A118897 
               A098056
%Y A118890 Adjacent sequences: A118887 A118888 A118889 this_sequence A118891 A118892 
               A118893
%K A118890 nonn,tabf
%O A118890 0,2
%A A118890 Emeric Deutsch (deutsch(AT)duke.poly.edu), May 04 2006