OFFSET
0,6
COMMENTS
a(n) is the least integer k such that k/Fibonacci(n) > 1/3.
LINKS
Clark Kimberling, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,0,0,0,1,-1,-1)
FORMULA
G.f.: -((x (-1 + x^2 + x^3 + x^7 + x^8))/((-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.
MATHEMATICA
LinearRecurrence[{1, 1, 0, 0, 0, 0, 0, 1, -1, -1}, {0, 1, 1, 1, 1, 2, 3, 5, 7, 12}, 50] (* Harvey P. Dale, Oct 18 2018 *)
Table[Ceiling[Fibonacci[n]/3], {n, 0, 20}] (* Eric W. Weisstein, Feb 07 2025 *)
Ceiling[Fibonacci[Range[0, 20]]/3] (* Eric W. Weisstein, Feb 07 2025 *)
CoefficientList[Series[-x (-1 + x^2 + x^3 + x^7 + x^8)/((-1 + x) (1 + x) (1 + x^2) (-1 + x + x^2) (1 + x^4)), {x, 0, 20}], x] (* Eric W. Weisstein, Feb 07 2025 *)
Table[(9 - 6 Cos[n Pi/2] + 8 Fibonacci[n] - (-1)^n (3 + 4 Sin[n Pi/4] (Cos[n Pi/2] + Sqrt[2] Sin[n Pi/2])))/24, {n, 0, 20}] (* Eric W. Weisstein, Feb 07 2025 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 12 2017
STATUS
approved