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A293552
a(n) is the least integer k such that k/Fibonacci(n) > 1/4.
2
0, 1, 1, 1, 1, 2, 2, 4, 6, 9, 14, 23, 36, 59, 95, 153, 247, 400, 646, 1046, 1692, 2737, 4428, 7165, 11592, 18757, 30349, 49105, 79453, 128558, 208010, 336568, 544578, 881145, 1425722, 2306867, 3732588, 6039455, 9772043, 15811497, 25583539, 41395036, 66978574
OFFSET
0,6
LINKS
FORMULA
G.f.: -((x (-1 + x^2 + x^3 + x^5 + x^6))/((-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) = ceiling(Fibonacci(n)/4).
a(n) = A004697(n) + 1 for n > 0.
MATHEMATICA
z = 120; r = 1/4; f[n_] := Fibonacci[n];
Table[Floor[r*f[n]], {n, 0, z}]; (* A004697 *)
Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293552 *)
Table[Round[r*f[n]], {n, 0, z}]; (* A293553 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 14 2017
STATUS
approved