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Search: id:A118357
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| A118357 |
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Triangle read by rows: T(n,k) is the number of ternary sequences of length n containing k subsequences 00 (n>=1, 0<=k<=n-1). |
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+0
2
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| 1, 3, 8, 1, 22, 4, 1, 60, 16, 4, 1, 164, 56, 18, 4, 1, 448, 188, 68, 20, 4, 1, 1224, 608, 248, 80, 22, 4, 1, 3344, 1920, 864, 312, 92, 24, 4, 1, 9136, 5952, 2928, 1152, 380, 104, 26, 4, 1, 24960, 18192, 9696, 4128, 1472, 452, 116, 28, 4, 1, 68192, 54976, 31536, 14400
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Sum of entries in row n is 3^n (A000244). T(n,0)=A028859(n). T(n,1)=A073388(n-2). Sum(k*T(n,k),k=0..n-1)=(n-1)*3^(n-2) (A027471).
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FORMULA
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G.f.=G-1, where G=G(t,z)=[1+(1-t)z]/[1-(2+t)z-2(1-t)z^2]. G.f. of column k is z^(k+1)*(1-2z)^(k-1)/(1-2z-2z^2)^(k+1) (k>=1).
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EXAMPLE
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T(4,2)=2 because we have 0001, 0002, 1000, and 2000.
Triangle starts:
3;
8,1;
22,4,1;
60,16,4,1;
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MAPLE
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G:=(1+(1-t)*z)/(1-(2+t)*z-2*(1-t)*z^2): 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: for n from 1 to 12 do seq(coeff(P[n], t, j), j=0..n-1) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A000244, A028859, A073388, A027471.
Adjacent sequences: A118354 A118355 A118356 this_sequence A118358 A118359 A118360
Sequence in context: A132338 A132702 A022833 this_sequence A010627 A103712 A132019
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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 24 2006
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