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A087567 a(n) = (1/5)*Sum_{k=0..n} binomial(n,k)*Fibonacci(k)*5^k. 1
1, 7, 68, 609, 5555, 50456, 458737, 4169823, 37904764, 344559985, 3132110411, 28471412592, 258809985953, 2352626740919, 21385776919540, 194400346514241, 1767132187070947, 16063531893267208, 146020234807218449, 1327348749622606095, 12065825708695393196 (list; graph; refs; listen; history; text; internal format)
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).

a(n) = -(7/50)*(7/2 - (5/2)*sqrt(5))^n*sqrt(5) + (7/50)*sqrt(5)*(7/2 + (5/2)*sqrt(5))^n + (1/2)*(7/2 - (5/2)*sqrt(5))^n + (1/2)*(7/2 + (5/2)*sqrt(5))^n, with n >= 0. - Paolo P. Lava, Jun 25 2008

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

PROG

(Sage) [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 * A328046 A306386 A136629

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

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Last modified February 19 19:06 EST 2020. Contains 332047 sequences. (Running on oeis4.)