Search: id:A119825
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%I A119825
%S A119825 1,3,9,26,1,76,4,1,222,16,4,1,648,60,16,4,1,1892,212,62,16,4,1,5524,728,
%T A119825 224,64,16,4,1,16128,2444,788,236,66,16,4,1,47088,8064,2712,848,248,68,
%U A119825 16,4,1,137480,26256,9168,2984,908,260,70,16,4,1,401392,84576,30576
%N A119825 Triangle read by rows: T(n,k) is the number of ternary sequences of length 
               n containing k subsequences 000 (consecutively; n,k>=0).
%C A119825 Rows 0 and 1 have one term each; row n (n>=2) have n-1 terms. Sum of 
               entries in row n is 3^n (A000244). T(n,0)=A119826(n) T(n,1)=A119827(n) 
               Sum(k*T(n,k),k>=0)=(n-2)*3^(n-3)=A027741(n-1).
%F A119825 G.f.=G(t,z)=[1+(1-t)z+(1-t)z^2]/[1-(2+t)z-2(1-t)z^2-2(1-t)z^3]
%e A119825 T(5,2)=4 because we have 00001,00002,10000 and 20000.
%e A119825 Triangle starts:
%e A119825 1;
%e A119825 3;
%e A119825 9;
%e A119825 26,1;
%e A119825 76,4,1;
%e A119825 222,16,4,1;
%p A119825 G:=(1+(1-t)*z+(1-t)*z^2)/(1-(2+t)*z-2*(1-t)*z^2-2*(1-t)*z^3): Gser:=simplify(series(G,
               z=0,15)): P[0]:=1: for n from 1 to 12 do P[n]:=sort(coeff(Gser,z^n)) 
               od: 1;3;for n from 2 to 12 do seq(coeff(P[n],t,j),j=0..n-2) od; # 
               yields sequence in triangular form
%Y A119825 Cf. A000244, A119826, A119827, A027741.
%Y A119825 Sequence in context: A006204 A013572 A119851 this_sequence A037260 A035313 
               A055293
%Y A119825 Adjacent sequences: A119822 A119823 A119824 this_sequence A119826 A119827 
               A119828
%K A119825 nonn,tabf
%O A119825 0,2
%A A119825 Emeric Deutsch (deutsch(AT)duke.poly.edu), May 26 2006

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