A293547 - OEIS

A293547

a(n) is the integer k that minimizes |k/Fibonacci(n) - 2/3|.

0, 1, 1, 1, 2, 3, 5, 9, 14, 23, 37, 59, 96, 155, 251, 407, 658, 1065, 1723, 2787, 4510, 7297, 11807, 19105, 30912, 50017, 80929, 130945, 211874, 342819, 554693, 897513, 1452206, 2349719, 3801925, 6151643, 9953568, 16105211, 26058779, 42163991, 68222770

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OFFSET

0,5

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1, 1, 0, -1, 1, 1)

FORMULA

G.f.: -((x (1 - x^2 + x^4))/((-1 + x + x^2) (1 + x^4))).

a(n) = a(n-1) + a(n-2) - a(n-4) + a(n-5) + a(n-6) for n >= 7.

a(n) = floor(1/2 + 2*Fibonacci(n)/3).

a(n) = A293545(n) if (fractional part of 2*Fibonacci(n)/3) < 1/2, otherwise a(n) = A293546(n).

MATHEMATICA