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A258321
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a(n) = Fibonacci(n) + n*Lucas(n).
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2
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0, 2, 7, 14, 31, 60, 116, 216, 397, 718, 1285, 2278, 4008, 7006, 12179, 21070, 36299, 62304, 106588, 181812, 309305, 524942, 888977, 1502474, 2534736, 4269050, 7178911, 12054926, 20215927, 33859908, 56646980, 94667088, 158045413, 263604046, 439272349
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: x*(2 + 3*x - 2*x^2)/(1 - x - x^2)^2.
a(n) = -a(-n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - a(n-4).
a(n) = (n+1)*Fibonacci(n+1) + (n-1)*Fibonacci(n-1).
Sum_{i>0} 1/a(i) = .782177794921758720...
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MATHEMATICA
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Table[Fibonacci[n] + n LucasL[n], {n, 0, 40}] (* or *) LinearRecurrence[{2, 1, -2, -1}, {0, 2, 7, 14}, 40]
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PROG
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(Sage) [fibonacci(n)+n*lucas_number2(n, 1, -1) for n in (0..40)]
(Magma) [Fibonacci(n)+n*Lucas(n): n in [0..40]]
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CROSSREFS
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Cf. A061705: n*Fibonacci(n)+Lucas(n) = (n+1)*Fibonacci(n+1)-(n-1)*Fibonacci(n-1) with n>0.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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