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A293632
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Least integer k such that k/Fibonacci(n) >= 3/4.
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3
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1, 1, 2, 3, 4, 6, 10, 16, 26, 42, 67, 108, 175, 283, 458, 741, 1198, 1938, 3136, 5074, 8210, 13284, 21493, 34776, 56269, 91045, 147314, 238359, 385672, 624030, 1009702, 1633732, 2643434, 4277166, 6920599, 11197764, 18118363, 29316127, 47434490, 76750617
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OFFSET
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1,3
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LINKS
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FORMULA
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G.f.: x*(1 - x + x^2 - x^3 - x^5)/((1 - x)*(1 - x + x^2)*(1 - x - x^2)*(1 + x + x^2)).
a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) - a(n-7) for n >= 8.
a(n) = ceiling(3*Fibonacci(n)/4).
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EXAMPLE
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For n=8, (3/4)*Fibonacci(8) = (3/4)*21 = 15.75 hence a(8) = 16.
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MATHEMATICA
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z = 120; r = 3/4; f[n_] := Fibonacci[n];
Table[Floor[r*f[n]], {n, 1, z}]; (* A293631 *)
Table[Ceiling[r*f[n]], {n, 1, z}]; (* A293632 *)
Table[Round[r*f[n]], {n, 1, z}]; (* A293633 *)
LinearRecurrence[{2, -1, 1, -1, 1, 0, -1}, {1, 1, 2, 3, 4, 6, 10}, 40] (* Bruno Berselli, Feb 16 2018 *)
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PROG
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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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