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Search: id:A119825
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| A119825 |
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Triangle read by rows: T(n,k) is the number of ternary sequences of length n containing k subsequences 000 (consecutively; n,k>=0). |
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+0
3
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| 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, 224, 64, 16, 4, 1, 16128, 2444, 788, 236, 66, 16, 4, 1, 47088, 8064, 2712, 848, 248, 68, 16, 4, 1, 137480, 26256, 9168, 2984, 908, 260, 70, 16, 4, 1, 401392, 84576, 30576
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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).
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FORMULA
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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]
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EXAMPLE
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T(5,2)=4 because we have 00001,00002,10000 and 20000.
Triangle starts:
1;
3;
9;
26,1;
76,4,1;
222,16,4,1;
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MAPLE
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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
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CROSSREFS
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Cf. A000244, A119826, A119827, A027741.
Sequence in context: A006204 A013572 A119851 this_sequence A037260 A035313 A055293
Adjacent sequences: A119822 A119823 A119824 this_sequence A119826 A119827 A119828
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KEYWORD
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nonn,tabf
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), May 26 2006
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