A293631 - OEIS

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A293631

Greatest integer k such that k/Fibonacci(n) <= 3/4.

0, 0, 1, 2, 3, 6, 9, 15, 25, 41, 66, 108, 174, 282, 457, 740, 1197, 1938, 3135, 5073, 8209, 13283, 21492, 34776, 56268, 91044, 147313, 238358, 385671, 624030, 1009701, 1633731, 2643433, 4277165, 6920598, 11197764, 18118362, 29316126, 47434489, 76750616

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OFFSET

1,4

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000

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

FORMULA

G.f.: x^3*(1 + x + x^3)/((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) = floor(3*Fibonacci(n)/4).

a(n) = A293632(n) if n = (0 mod 6), else, a(n) = A293632(n) - 1.

EXAMPLE