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 A293631 Greatest integer k such that k/Fibonacci(n) <= 3/4. 3
 0, 0, 1, 2, 3, 6, 9, 15, 25, 41, 66, 108, 174, 282, 457, 740, 1197, 1938, 3135, 5073, 8209, 13283, 21492, 34776, 56268, 91044, 147313, 238358, 385671, 624030, 1009701, 1633731, 2643433, 4277165, 6920598, 11197764, 18118362, 29316126, 47434489, 76750616 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Clark Kimberling, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,0,1,-1,-1). FORMULA G.f.: x^3*(1 + x + x^3)/((1 - x)*(1 + x)*(1 - x + x^2)*(1 - x - x^2)*(1 + x + x^2)). a(n) = a(n-1) + a(n-2) + a(n-6) - a(n-7) - a(n-8) for n >= 9. a(n) = floor(3*Fibonacci(n)/4). a(n) = A293632(n) if n = (0 mod 6), else, a(n) = A293632(n) - 1. EXAMPLE For n=8, (3/4)*Fibonacci(8) = (3/4)*21 = 15.75 hence a(8) = 15. MATHEMATICA 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[{1, 1, 0, 0, 0, 1, -1, -1}, {0, 0, 1, 2, 3, 6, 9, 15}, 40] (* Bruno Berselli, Feb 16 2018 *) PROG (PARI) a(n) = floor(3*fibonacci(n)/4); \\ Andrew Howroyd, Feb 12 2018 CROSSREFS Cf. A000045, A293632, A293633. Sequence in context: A192671 A080239 A114323 * A018158 A057928 A026735 Adjacent sequences:  A293628 A293629 A293630 * A293632 A293633 A293634 KEYWORD nonn,easy AUTHOR Clark Kimberling, Oct 14 2017 EXTENSIONS Offset changed to 1 by Clark Kimberling, Feb 12 2018 STATUS approved

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Last modified February 20 19:41 EST 2020. Contains 332084 sequences. (Running on oeis4.)