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A099256
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Expansion of g.f. (3-x)*(1+3*x+x^2)/((1-x-x^2)*(1+x-x^2)).
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2
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3, 8, 9, 23, 24, 61, 63, 160, 165, 419, 432, 1097, 1131, 2872, 2961, 7519, 7752, 19685, 20295, 51536, 53133, 134923, 139104, 353233, 364179, 924776, 953433, 2421095, 2496120, 6338509, 6534927, 16594432, 17108661, 43444787, 44791056, 113739929, 117264507, 297775000, 307002465, 779585071
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OFFSET
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0,1
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COMMENTS
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One of two sequences involving the Lucas/Fibonacci numbers. This sequence consists of pairs of numbers more or less close to each other with "jumps" in between pairs.
a(n+3) + a(n) - a(n+2) appears to be mysteriously connected with a(n+1).
Both this sequence and A099255 were created using "Floretion dynamical symmetries" (see link for further details).
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LINKS
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FORMULA
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a(2n+2) - a(2n+1) = Fibonacci(2n-1).
a(0) = 3, a(1) = 8, a(2) = 9, a(3) = 23, a(n+4) = 3a(n+2) - a(n).
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MATHEMATICA
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LinearRecurrence[{0, 3, 0, -1}, {3, 8, 9, 23}, 40] (* Harvey P. Dale, Apr 22 2012 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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