A214286 a(n) = floor(Fibonacci(n)/7).

0, 0, 0, 0, 0, 0, 1, 1, 3, 4, 7, 12, 20, 33, 53, 87, 141, 228, 369, 597, 966, 1563, 2530, 4093, 6624, 10717, 17341, 28059, 45401, 73461, 118862, 192324, 311187, 503511, 814698, 1318209, 2132907, 3451116, 5584024, 9035140, 14619165

Offset: 0

Author

Vincenzo Librandi, Jul 10 2012

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, 1, -1, -1).

Crossrefs

Cf. A004695-A004699.

Programs

Magma

[Floor(Fibonacci(n)/7): n in [0..40]];

Mathematica

Floor[Fibonacci[Range[0, 40]]/7] (* modified by G. C. Greubel, May 22 2019 *)
LinearRecurrence[{1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,-1},{0,0,0,0,0,0,1,1,3,4,7,12,20,33,53,87,141,228},50] (* Harvey P. Dale, Dec 01 2020 *)

PARI

vector(40, n, n--; fibonacci(n)\7 ) \\ G. C. Greubel, May 22 2019

Sage

[floor(fibonacci(n)/7) for n in (0..40)] # G. C. Greubel, May 22 2019

Formula

G.f.: x^6*(1+x^2+x^5+x^6+x^7+x^9+x^10) / ( (1-x-x^2)*(1-x^16) ). - R. J. Mathar, Jul 14 2012

a(n) = (A000045(n) - A105870(n))/7. - R. J. Mathar, Jul 14 2012