A293671 - OEIS

%I #10 Jul 07 2024 12:50:45

%S 0,0,0,1,2,4,6,10,16,27,44,71,115,186,301,488,789,1277,2067,3344,5412,

%T 8756,14168,22925,37094,60020,97114,157134,254248,411383,665632,

%U 1077015,1742647,2819662,4562309,7381972,11944281,19326253,31270535,50596788,81867324

%N a(n) is the greatest integer k such that k/Fibonacci(n) < 4/5.

%H Clark Kimberling, <a href="/A293671/b293671.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (1, 2, -1, -2, 2, 1, -3, -1, 3, 0, -2, 1, 2, -1, -1)

%F 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)).

%F 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.

%F a(n) = floor(4*Fibonacci(n)/5).

%F a(n) = A293672(n) - 1 for n > 0.

%t z = 120; r = 4/5; f[n_] := Fibonacci[n];

%t Table[Floor[r*f[n]], {n, 0, z}];   (* A293671 *)

%t Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293672 *)

%t Table[Round[r*f[n]], {n, 0, z}];   (* A293673 *)

%t 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 *)

%Y Cf. A000045, A293672, A293673.

%K nonn,easy

%O 0,5

%A _Clark Kimberling_, Oct 15 2017