A087453 a(n) = S(n,5), where S(n,m) = Sum_{k=0..n} binomial(n,k)*Fibonacci(m*k).

0, 5, 65, 790, 9555, 115525, 1396720, 16886585, 204161685, 2468349470, 29842764575, 360804095305, 4362182828640, 52739531723965, 637629901296505, 7709053867890950, 93203771368320795, 1126849435241369885, 13623801173086279760, 164714071462466568145

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..923

Index entries for linear recurrences with constant coefficients, signature (13,-11).

Formula

a(n) = 13*a(n-1)-11*a(n-2).

a(n) = (1/sqrt(5))*(((13+5*sqrt(5))/2)^n-((13-5*sqrt(5))/2)^n).

G.f.: 5*x / (11*x^2-13*x+1). - Colin Barker, Apr 27 2015

Mathematica

Table[Sum[Binomial[n, k]Fibonacci[5k], {k, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Sep 03 2014 *)
LinearRecurrence[{13, -11}, {0, 5}, 20] (* Vincenzo Librandi, Apr 27 2015 *)

Prog

(PARI) concat(0, Vec(5*x/(11*x^2-13*x+1) + O(x^100))) \\ Colin Barker, Apr 27 2015
(Magma) I:=[0, 5]; [n le 2 select I[n] else 13*Self(n-1)-11*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Apr 27 2015

Crossrefs

Cf. A001906 (S(n,1)), A030191 (S(n,2)).

Sequence in context: A236321 A199024 A155653 * A103974 A233093 A208588

Adjacent sequences: A087450 A087451 A087452 * A087454 A087455 A087456

Keyword

nonn,easy

Author

Benoit Cloitre, Oct 23 2003

Status

approved