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A173673
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a(2k) = floor(F(k)/2), a(2k+1) = ceiling(F(k)/2), where F = A000045 is the Fibonacci sequence.
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1
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0, 0, 0, 1, 0, 1, 1, 1, 1, 2, 2, 3, 4, 4, 6, 7, 10, 11, 17, 17, 27, 28, 44, 45, 72, 72, 116, 117, 188, 189, 305, 305, 493, 494, 798, 799, 1292, 1292, 2090, 2091, 3382, 3383, 5473, 5473, 8855, 8856, 14328, 14329, 23184, 23184, 37512, 37513, 60696, 60697, 98209, 98209, 158905, 158906, 257114, 257115, 416020, 416020
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OFFSET
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0,10
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COMMENTS
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Original definition: Paired sequence: {male,female} ={Floor[A000045(n)/2],A000045[n]-Floor[A000045(n)/2]}
Shows excess of females over males in Fibonacci sequences.
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LINKS
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FORMULA
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a(2k) = floor(Fibonacci(k)/2), a(2k+1) = ceiling(Fibonacci(k)/2) = Fibonacci(k)-a(2k).
Empirical g.f.: x^3*(1+x+x^2+2*x^3+x^4+x^5) / ((1+x)*(1-x+x^2)*(1+x+x^2)*(1-x^2-x^4)). - Colin Barker, Aug 02 2016
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MATHEMATICA
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Table[{Floor[Fibonacci[j]/
2], Fibonacci[j] - Floor[Fibonacci[j]/2]}, {j, 0, 30}]
Flatten[%]
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PROG
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(PARI) a(n)=(fibonacci(n\2)+n%2)\2 \\ M. F. Hasler, Nov 24 2010
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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