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Search: id:A118897
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| A118897 |
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Triangle read by rows: T(n,k) is the number of binary sequences of length n containing k subsequences 0000 (n,k>=0). |
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2
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| 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, 5, 2, 1, 773, 136, 65, 30, 12, 5, 2, 1, 1490, 294, 145, 68, 31, 12, 5, 2, 1, 2872, 628, 319, 154, 71, 32, 12, 5, 2, 1, 5536, 1328, 694, 344, 163, 74, 33, 12, 5, 2, 1, 10671, 2787
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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).
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FORMULA
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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)].
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EXAMPLE
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T(7,2)=5 because we have 0000010,0000011,0100000,1100000, and 1000001.
Triangle starts:
1;
2;
4;
8;
15,1;
29,2,1;
56,5,2,1;
108,12,5,2,1;
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MAPLE
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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
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CROSSREFS
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Cf. A000079, A000078, A118898, A011787.
Sequence in context: A118884 A118890 A118869 this_sequence A098056 A097100 A002954
Adjacent sequences: A118894 A118895 A118896 this_sequence A118898 A118899 A118900
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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 04 2006
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