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Search: id:A118884
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| A118884 |
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Triangle read by rows: T(n,k) is the number of binary sequences of length n containing k subsequences 0011 (n,k>=0). |
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+0
2
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| 1, 2, 4, 8, 15, 1, 28, 4, 52, 12, 96, 32, 177, 78, 1, 326, 180, 6, 600, 400, 24, 1104, 864, 80, 2031, 1827, 237, 1, 3736, 3800, 648, 8, 6872, 7800, 1672, 40, 12640, 15840, 4128, 160, 23249, 31884, 9846, 556, 1, 42762, 63704, 22844, 1752, 10, 78652, 126480
(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 1+floor(n/4) terms. Sum of entries in row n is 2^n (A000079). T(n,0)=A008937(n+1). T(n,1)=A118885(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/[1-2z+(1-t)z^4]. T(n,k)=2T(n-1,k)-T(n-4,k)+T(n-4,k-1) (n>=4,k>=1).
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EXAMPLE
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T(9,2)=6 because we have aa0,aa1,a0a,a1a,0aa, and 1aa, where a=0011.
Triangle starts:
1;
2;
4;
8;
15,1;
28,4;
52,12;
96,32;
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MAPLE
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G:=1/(1-2*z+(1-t)*z^4): Gser:=simplify(series(G, z=0, 23)): P[0]:=1: for n from 1 to 19 do P[n]:=sort(coeff(Gser, z^n)) od: for n from 0 to 19 do seq(coeff(P[n], t, j), j=0..floor(n/4)) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A000079, A008937, A118885, A001787.
Sequence in context: A130711 A093483 A028398 this_sequence A118890 A118869 A118897
Adjacent sequences: A118881 A118882 A118883 this_sequence A118885 A118886 A118887
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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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