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A102026
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Number of n-bit strings that contain no more than 4 zeros and no more than 2 leading and 2 trailing zeros.
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2
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2, 4, 7, 13, 25, 49, 97, 191, 375, 737, 1449, 2849, 5601, 11011, 21647, 42557, 83665, 164481, 323361, 635711, 1249775, 2456993, 4830321, 9496161, 18668961, 36702211, 72154647, 141852301, 278874281, 548252401, 1077835841, 2118969471
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OFFSET
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1,1
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COMMENTS
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Used in the NRZ encoding to avoid substrings of more than 4 zeros.
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REFERENCES
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Raphael Reischuk, On avoiding monochrome substrings of length 5.
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LINKS
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FORMULA
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G.f.: 2*x+4*x^2 -x^3*(7+6*x+5*x^2+4*x^3+3*x^4) / ( -1+x+x^2+x^3+x^4+x^5 ). - R. J. Mathar, Oct 27 2012
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EXAMPLE
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a(3) = 2^3 - 1 = 7, since '000' is not a valid string, but all others are.
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MATHEMATICA
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m[x_] := If[x <= 4, 2^x,
If[x == 5, 31,
m[x - 1] + m[x - 2] + m[x - 3] + m[x - 4] + m[x - 5]]]
c[x_] := If[x <= 2, 0,
If[x == 3, 1,
If[x == 4, 3,
If[x == 5, 6,
If[x == 6, 12,
If[x == 7, 23,
If[x == 8, 45, 2*c[x - 1] - c[x - 6]]]]]]]]
valid[x_] := m[x] - c[x]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Raphael Reischuk (raphael(AT)stud.uni-saarland.de), Jun 18 2007
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STATUS
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approved
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