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A293545
a(n) is the greatest integer k such that k/Fibonacci(n) < 2/3.
3
0, 0, 0, 1, 2, 3, 5, 8, 14, 22, 36, 59, 96, 155, 251, 406, 658, 1064, 1722, 2787, 4510, 7297, 11807, 19104, 30912, 50016, 80928, 130945, 211874, 342819, 554693, 897512, 1452206, 2349718, 3801924, 6151643, 9953568, 16105211, 26058779, 42163990, 68222770
OFFSET
0,5
LINKS
Index entries for linear recurrences with constant coefficients, signature (1, 1, 0, 0, 0, 0, 0, 1, -1, -1)
FORMULA
G.f.: (x^3 (1 + x + x^2) (1 - x^2 + x^3))/((-1 + x) (1 + x) (1 + x^2) (-1 + x + x^2) (1 + x^4)).
a(n) = a(n-1) + a(n-2) + a(n-8) - a(n-9) - a(n-10) for n >= 11.
a(n) = floor(2*Fibonacci(n)/3).
a(n) = A293546(n) - 1 for n > 0.
MATHEMATICA
z = 120; r = 2/3; f[n_] := Fibonacci[n];
Table[Floor[r*f[n]], {n, 0, z}]; (* A293545 *)
Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293546 *)
Table[Round[r*f[n]], {n, 0, z}]; (* A293547 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 12 2017
STATUS
approved