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A293644
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a(n) is the integer k that minimizes |k/Fibonacci(n) - 3/5|.
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3
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0, 1, 1, 1, 2, 3, 5, 8, 13, 20, 33, 53, 86, 140, 226, 366, 592, 958, 1550, 2509, 4059, 6568, 10627, 17194, 27821, 45015, 72836, 117851, 190687, 308537, 499224, 807761, 1306985, 2114747, 3421732, 5536479, 8958211, 14494690, 23452901, 37947592, 61400493
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OFFSET
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0,5
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LINKS
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Clark Kimberling, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1, 2, -1, -2, 1, 2, -1, -2, 1, 1)
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FORMULA
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G.f.: -(((-1 + x)^2 x (1 + x)^2 (1 + x^4))/((-1 + x + x^2) (1 - x^2 + x^4 - x^6 + x^8))).
a(n) = a(n-1) + 2 a(n-2) - a(n-3) - 2 a(n-4) + a(n-5) + 2 a(n-6) - a(n-7) - 2 a(n-8) + a(n-9) + a(n-10) for n >= 11.
a(n) = floor(1/2 + 3*Fibonacci(n)/5).
a(n) = A293642(n) if (fractional part of 3*Fibonacci(n)/5) < 1/2, otherwise a(n) = A293643(n).
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MATHEMATICA
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z = 120; r = 3/5; f[n_] := Fibonacci[n];
Table[Floor[r*f[n]], {n, 0, z}]; (* A293642 *)
Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293643 *)
Table[Round[r*f[n]], {n, 0, z}]; (* A293644 *)
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CROSSREFS
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Cf. A000045, A293642, A293643.
Sequence in context: A013985 A092834 A080106 * A158415 A005347 A100582
Adjacent sequences: A293641 A293642 A293643 * A293645 A293646 A293647
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KEYWORD
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nonn,easy
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AUTHOR
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Clark Kimberling, Oct 14 2017
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STATUS
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approved
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