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A066067
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Number of binary strings u of any length with property that length(u) + number of 0's in u <= n (only one of a string and its reversal are counted).
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2
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1, 2, 3, 6, 10, 18, 29, 49, 78, 128, 203, 329, 523, 844, 1347, 2172, 3480, 5614, 9023, 14567, 23466, 37910, 61165, 98865, 159677, 258190, 417283, 674890, 1091214, 1765146, 2854793, 4618373, 7470614, 12086436, 19552903, 31635193, 51181367, 82809832
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| If 0 is replaced by 2 (as in A007931) "length + 0-bits" is simply the total of ternary digits (e.g. 3 for 21 instead of 01).
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (3,-1,-4,4,-2,1,1,-1)
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FORMULA
| G.f.: x(-x^7-x^4+3x^3-2x^2-x+1)/[(1-x-x^2)(1-x^2-x^4)(1-x)^2].
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EXAMPLE
| a(3) = 3: 0 01 111 (e.g. 01: length 2 + 1 zero = 3)
a(4) = 6: 0 01 00 011 101 1111
a(5) =10: 0 01 00 011 101 001 010 0111 1011 11111
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MATHEMATICA
| CoefficientList[Series[x (-x^7-x^4+3x^3-2x^2-x+1)/((1-x-x^2) (1-x^2-x^4) (1-x)^2), {x, 0, 50}], x] (* From Harvey P. Dale, Jun 15 2011 *)
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CROSSREFS
| If reversals are counted as distinct then we obtain A000126.
A007931 (binary strings represented by ternary numbers),
Cf. A035615 (binary "same game").
Sequence in context: A081028 A065441 A075531 * A121364 A172516 A102702
Adjacent sequences: A066064 A066065 A066066 * A066068 A066069 A066070
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KEYWORD
| nonn
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AUTHOR
| Frank.Ellermann(AT)t-online.de, Dec 02 2001
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EXTENSIONS
| More terms from Harvey P. Dale, June 15 2011.
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