OFFSET
0,6
LINKS
Clark Kimberling, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1, 2, -1, -2, 1, 2, -1, -2, 1, 1)
FORMULA
G.f.: -((x^3 (1 - x^2 + x^4))/((-1 + x + x^2) (1 - x^2 + x^4 - x^6 + x^8))).
a(n) = a(n-1) + 2 a(n-2) - a(n-3) - 2 a(n-4) + a(n-5) + 2 a(n-6) - a(n-7) - 2 a(n-8) + a(n-9) + a(n-10) for n >= 11.
a(n) = floor(1/2 + 2*Fibonacci(n)/5).
MATHEMATICA
z = 120; r = 2/5; f[n_] := Fibonacci[n];
Table[Floor[r*f[n]], {n, 0, z}]; (* A293639 *)
Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293640 *)
Table[Round[r*f[n]], {n, 0, z}]; (* A293641 *)
LinearRecurrence[{1, 2, -1, -2, 1, 2, -1, -2, 1, 1}, {0, 0, 0, 1, 1, 2, 3, 5, 8, 14}, 50] (* Harvey P. Dale, May 15 2025 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 14 2017
STATUS
approved