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A143361
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Triangle read by rows: T(n,k) is the number of 010-avoiding binary words of length n containing k 00 subwords (0<=k<=n-1).
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0
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2, 3, 1, 4, 2, 1, 6, 3, 2, 1, 9, 6, 3, 2, 1, 13, 11, 7, 3, 2, 1, 19, 18, 14, 8, 3, 2, 1, 28, 30, 24, 17, 9, 3, 2, 1, 41, 50, 43, 30, 20, 10, 3, 2, 1, 60, 81, 77, 57, 36, 23, 11, 3, 2, 1, 88, 130, 132, 108, 72, 42, 26, 12, 3, 2, 1, 129, 208, 224, 193, 143, 88, 48, 29, 13, 3, 2, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Sum of entries in row n = A005251(n+3).
T(n,0)=A000930(n+2).
Sum(k*T(n,k),k=0..n-1)=A118430(n+1).
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FORMULA
| G.f.=G=G(t,z)=(1+z-tz+z^2)/(1-z-tz+tz^2-z^3)-1.
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EXAMPLE
| T(5,2)=3 because we have 00011, 10001 and 11000.
Triangle starts:
2;
3,1;
4,2,1;
6,3,2,1;
9,6,3,2,1;
13,11,7,3,2,1;
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MAPLE
| G:=(1+z-t*z+z^2)/(1-z-t*z+t*z^2-z^3)-1: Gser:=simplify(series(G, z=0, 14)): for n to 12 do P[n]:=sort(coeff(Gser, z, n)) end do: for n to 12 do seq(coeff(P[n], t, j), j=0..n-1) end do; # yields sequence in triangular form
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CROSSREFS
| Cf. A005251, A000930, A118430.
Sequence in context: A195164 A087088 A104705 * A152547 A083906 A160541
Adjacent sequences: A143358 A143359 A143360 * A143362 A143363 A143364
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KEYWORD
| nonn,tabl
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 15 2008
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