A087567 a(n) = (1/5)*Sum_{k=0..n} binomial(n,k)*Fibonacci(k)*5^k.

1, 7, 68, 609, 5555, 50456, 458737, 4169823, 37904764, 344559985, 3132110411, 28471412592, 258809985953, 2352626740919, 21385776919540, 194400346514241, 1767132187070947, 16063531893267208, 146020234807218449, 1327348749622606095, 12065825708695393196

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (7,19).

Formula

a(n) = 7*a(n-1) + 19*a(n-2).

G.f.: 1 / (-19*x^2-7*x+1). - Colin Barker, Aug 08 2013

From Amiram Eldar, Jan 18 2026: (Start)

a(n) = (((7+5*sqrt(5))/2)^(n+1) - ((7-5*sqrt(5))/2)^(n+1))/(5*sqrt(5)).

E.g.f.: exp(7*x/2) * (cosh(5*sqrt(5)*x/2) + (7/(5*sqrt(5))) * sinh(5*sqrt(5)*x/2)). (End)

Mathematica

LinearRecurrence[{7, 19}, {1, 7}, 25] (* Paolo Xausa, Jan 07 2024 *)

Prog

(SageMath) [lucas_number1(n, 7, -19) for n in range(1, 20)] # Zerinvary Lajos, Apr 29 2009

Crossrefs

Cf. A014445, A057088, A015553.

Sequence in context: A294664 A120079 A297502 * A390334 A328046 A379521

Adjacent sequences: A087564 A087565 A087566 * A087568 A087569 A087570

Keyword

nonn,easy

Author

Benoit Cloitre, Oct 25 2003

Extensions

More terms from Colin Barker, Aug 08 2013

Status

approved