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A293671
a(n) is the greatest integer k such that k/Fibonacci(n) < 4/5.
4
0, 0, 0, 1, 2, 4, 6, 10, 16, 27, 44, 71, 115, 186, 301, 488, 789, 1277, 2067, 3344, 5412, 8756, 14168, 22925, 37094, 60020, 97114, 157134, 254248, 411383, 665632, 1077015, 1742647, 2819662, 4562309, 7381972, 11944281, 19326253, 31270535, 50596788, 81867324
OFFSET
0,5
LINKS
Index entries for linear recurrences with constant coefficients, signature (1, 2, -1, -2, 2, 1, -3, -1, 3, 0, -2, 1, 2, -1, -1)
FORMULA
G.f.: (x^3 (1 + x - x^3 + x^10))/((-1 + x) (-1 + x + x^2) (1 + x + x^2 + x^3 + x^4) (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) + 2 a(n-5) + a(n-6) - 3 a(n-7) - a(n-8) + 3 a(n-9) - 2 a(n-11) + a(n-12) + 2 a(n-13) - a(n-14) - a(n-15) for n >= 16.
a(n) = floor(4*Fibonacci(n)/5).
a(n) = A293672(n) - 1 for n > 0.
MATHEMATICA
z = 120; r = 4/5; f[n_] := Fibonacci[n];
Table[Floor[r*f[n]], {n, 0, z}]; (* A293671 *)
Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293672 *)
Table[Round[r*f[n]], {n, 0, z}]; (* A293673 *)
LinearRecurrence[{1, 2, -1, -2, 2, 1, -3, -1, 3, 0, -2, 1, 2, -1, -1}, {0, 0, 0, 1, 2, 4, 6, 10, 16, 27, 44, 71, 115, 186, 301}, 50] (* Harvey P. Dale, Jul 07 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 15 2017
STATUS
approved