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A103326 a(n) = Fibonacci(5n)/Fibonacci(n). 2
5, 55, 305, 2255, 15005, 104005, 709805, 4873055, 33379505, 228841255, 1568358005, 10750060805, 73681030805, 505019869255, 3461450947505, 23725155368255, 162614587921805, 1114577087604805, 7639424691459005, 52361396626646255, 358890349406803505 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5,15,-15,-5,1).

FORMULA

a(n) = L(4n) + (-1)^n*L(2n) + 1, where L(n) = A000032, the Lucas numbers.

a(n) = 1 + L(n)*L(3n). - Neven Juric, Jan 05 2009

a(n) = 25*(Fibonacci(n)^4 + (-1)^n*Fibonacci(n)^2) + 5. - Gary Detlefs, Dec 22 2012

G.f.: -5*x*(x^4-4*x^3-9*x^2+6*x+1) / ((x-1)*(x^2-7*x+1)*(x^2+3*x+1)). - Colin Barker, Jul 16 2013

a(n) = 5 * A088545(n). - Joerg Arndt, Jul 16 2013

exp( Sum_{n >= 1} a(n)*x^n/n ) = Sum_{n >= 0} A001656(n)*x^n. - Peter Bala, Mar 30 2015

a(n) = 1+(1/2*(7-3*sqrt(5)))^n+(1/2*(-3-sqrt(5)))^n+(1/2*(-3+sqrt(5)))^n+(1/2*(7+3*sqrt(5)))^n. - Colin Barker, Jun 03 2016

MAPLE

p:= (1+5^(1/2))/2: q:=(1-5^(1/2))/2:

seq(simplify(q^(4*n)+(p-2)^n+(q-2)^n+(3*p+2)^n+(-1)^(2*n)/4+3/4), n=1..19);

PROG

(MAGMA) [Fibonacci(5*n)/Fibonacci(n): n in [1..50]]; // Vincenzo Librandi, Apr 20 2011

(PARI) Vec(-5*x*(x^4-4*x^3-9*x^2+6*x+1)/((x-1)*(x^2-7*x+1)*(x^2+3*x+1)) + O(x^30)) \\ Colin Barker, Jun 03 2016

CROSSREFS

Fourth row of array A028412. Cf. A000032, A000045, A001656, A088545.

Sequence in context: A057722 A078216 A014700 * A060558 A014852 A144893

Adjacent sequences:  A103323 A103324 A103325 * A103327 A103328 A103329

KEYWORD

nonn,easy

AUTHOR

Ralf Stephan, Feb 03 2005

EXTENSIONS

More terms from Colin Barker, Jul 16 2013

STATUS

approved

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Last modified February 23 13:38 EST 2018. Contains 299581 sequences. (Running on oeis4.)