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Search: id:A118870
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| A118870 |
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Number of binary sequences of length n with no subsequence 0101. |
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+0
3
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| 1, 2, 4, 8, 15, 28, 53, 100, 188, 354, 667, 1256, 2365, 4454, 8388, 15796, 29747, 56020, 105497, 198672, 374140, 704582, 1326871, 2498768, 4705689, 8861770, 16688516, 31427872, 59185079, 111457548, 209897245, 395279228, 744391228, 1401840170
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Column 0 of A118869.
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FORMULA
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G.f.=(1+z^2)/[1-2z+z^2*(1-z)^2]. Recurrence relation: a(n)=2a(n-1)-a(n-2)+2a(n-3)-a(n-4) for n>=4.
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EXAMPLE
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a(5)=28 because among the 32 (=2^5) binary sequences of length 5 only 01010,01011,00101, and 10101 contain the subsequence 0101.
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MAPLE
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a[0]:=1:a[1]:=2:a[2]:=4:a[3]:=8: for n from 4 to 35 do a[n]:=2*a[n-1]-a[n-2]+2*a[n-3]-a[n-4] od: seq(a[n], n=0..35);
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CROSSREFS
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Cf. A118869, A005251, A000071, A000073.
Sequence in context: A008937 A128805 A049864 this_sequence A088532 A036621 A001383
Adjacent sequences: A118867 A118868 A118869 this_sequence A118871 A118872 A118873
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), May 03 2006
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