A004699 a(n) = floor(Fibonacci(n)/6).

0, 0, 0, 0, 0, 0, 1, 2, 3, 5, 9, 14, 24, 38, 62, 101, 164, 266, 430, 696, 1127, 1824, 2951, 4776, 7728, 12504, 20232, 32736, 52968, 85704, 138673, 224378, 363051, 587429, 950481, 1537910, 2488392, 4026302, 6514694, 10540997, 17055692, 27596690, 44652382

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1).

Crossrefs

Cf. A000045.

Programs

Magma

[Floor(Fibonacci(n)/6): n in [0..40]]; // Vincenzo Librandi, Jul 10 2012

Maple

seq(floor(combinat[fibonacci](n)/6), n=0..40); # Muniru A Asiru, Oct 10 2018

Mathematica

Table[Floor[Fibonacci[n]/6], {n, 0, 50}] (* Vincenzo Librandi, Jul 10 2012 *)
CoefficientList[Series[x^6 (1 + x + x^4 + x^6 + x^9 + x^10 + x^11 + x^14 + x^15 + x^17 + x^18)/((1 - x - x^2) (1 - x^24)), {x, 0, 50}], x] (* Stefano Spezia, Oct 11 2018 - corrected by G. C. Greubel, May 21 2019 *)

PARI

vector(50, n, n--; fibonacci(n)\6) \\ G. C. Greubel, Oct 09 2018

Sage

[floor(fibonacci(n)/6) for n in (0..40)] # G. C. Greubel, May 21 2019

Formula

G.f.: x^6*(1 + x + x^4 + x^6 + x^9 + x^10 + x^11 + x^14 + x^15 + x^17 + x^18)/((1 - x - x^2)*(1 - x^24)). [Corrected by G. C. Greubel, May 21 2019]

a(n) = (A000045(n) - A082117(n))/6. - R. J. Mathar, Jul 14 2012