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Search: id:A118869
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| A118869 |
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Triangle read by rows: T(n,k) is the number of binary sequences of length n containing k subsequences 0101 (n,k>=0). |
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+0
3
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| 1, 2, 4, 8, 15, 1, 28, 4, 53, 10, 1, 100, 24, 4, 188, 57, 10, 1, 354, 128, 26, 4, 667, 278, 68, 10, 1, 1256, 596, 164, 28, 4, 2365, 1260, 381, 79, 10, 1, 4454, 2628, 876, 200, 30, 4, 8388, 5430, 1977, 488, 90, 10, 1, 15796, 11136, 4380, 1184, 236, 32, 4, 29747, 22683
(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 floor(n/2) terms (n>=2). Sum of entries in row n is 2^n (A000079). T(n,0)=A118870(n). T(n,1)=A118871(n). Sum(k*T(n,k),k=0..n-1)=(n-3)*2^(n-4) (A001787).
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FORMULA
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G.f.=G(t,z)=[1+(1-t)z^2]/[1-2z+(1-t)z^2*(1-z)^2].
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EXAMPLE
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T(7,2)=4 because we have 0101010,0101011,0010101, and 1010101.
Triangle starts:
1;
2;
4;
8;
15,1;
28,4;
53,10,1;
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MAPLE
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G:=(1+(1-t)*z^2)/(1-2*z+(1-t)*z^2*(1-z)^2): Gser:=simplify(series(G, z=0, 20)): P[0]:=1: for n from 1 to 16 do P[n]:=coeff(Gser, z^n) od: 1; 2; for n from 1 to 16 do seq(coeff(P[n], t, j), j=0..floor(n/2)-1) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A000079, A118870, A118871, A001787, A118429.
Sequence in context: A028398 A118884 A118890 this_sequence A118897 A098056 A097100
Adjacent sequences: A118866 A118867 A118868 this_sequence A118870 A118871 A118872
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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 03 2006
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