A293639 - OEIS

%I #10 May 02 2019 16:19:42

%S 0,0,0,0,1,2,3,5,8,13,22,35,57,93,150,244,394,638,1033,1672,2706,4378,

%T 7084,11462,18547,30010,48557,78567,127124,205691,332816,538507,

%U 871323,1409831,2281154,3690986,5972140,9663126,15635267,25298394,40933662,66232056

%N a(n) is the greatest integer k such that k/Fibonacci(n) < 2/5.

%H Clark Kimberling, <a href="/A293639/b293639.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^4 (1 + x) (1 - x + x^2) (1 + x - x^2 - 2 x^3 + x^5 + x^6))/((-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(2*Fibonacci(n)/5).

%F a(n) = A293640(n) - 1 for n > 0.

%t z = 120; r = 2/5; f[n_] := Fibonacci[n];

%t Table[Floor[r*f[n]], {n, 0, z}];   (* A293639 *)

%t Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293640 *)

%t Table[Round[r*f[n]], {n, 0, z}];   (* A293641 *)

%t LinearRecurrence[{1,2,-1,-2,2,1,-3,-1,3,0,-2,1,2,-1,-1},{0,0,0,0,1,2,3,5,8,13,22,35,57,93,150},60] (* _Harvey P. Dale_, May 02 2019 *)

%Y Cf. A000045, A293640, A293641.

%K nonn,easy

%O 0,6

%A _Clark Kimberling_, Oct 14 2017