login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A065563 Product of three consecutive Fibonacci numbers. 11
2, 6, 30, 120, 520, 2184, 9282, 39270, 166430, 704880, 2986128, 12649104, 53583010, 226980390, 961505790, 4073001576, 17253515288, 73087057560, 309601753890, 1311494059590, 5555578014142, 23533806080736 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

Mohammad K. Azarian, Fibonacci Identities as Binomial Sums II, International Journal of Contemporary Mathematical Sciences, Vol. 7, No. 42, 2012, pp. 2053-2059.

Mohammad K. Azarian, Fibonacci Identities as Binomial Sums, International Journal of Contemporary Mathematical Sciences, Vol. 7, No. 38, 2012, pp. 1871-1876.

V. E. Hoggatt, D. A. Lind, "The Heights of Fibonacci Polynomials and an Associated Function", Fibonacci Quarterly, 5;2, April, 1967, pp. 141-152.

T. Koshy, Fibonacci and Lucas numbers with applications, Wiley, 2001, p. 89, No. 32, with a minus sign.

LINKS

Harry J. Smith, Table of n, a(n) for n=1..200

Index entries for linear recurrences with constant coefficients, signature (3,6,-3,-1).

FORMULA

a(n) = A000045(n)*A000045(n+1)*A000045(n+2).

G.f.: 2/(1 - 3*x - 6*x^2 + 3*x^3 + x^4).

a(n) = 2*A001655(n).

a(n) = Fibonacci(n+1)^3-(-1)^n*Fibonacci(n+1). - Gary Detlefs, Feb 02 2011

This corrects a sign mistake in the Koshy reference. - Wolfdieter Lang, Aug 07 2012

a(n) = 3*a(n-1) + 6*a(n-2) - 3*a(n-3) - a(n-4).

O.g.f.: 2*x/((1 + x - x^2)*(1 - 4*x - x^2)) (compare with A001655). - Wolfdieter Lang, Aug 06 2012

MAPLE

with (combinat):a:=n->fibonacci(n)*fibonacci(n+1)*fibonacci(n+2): seq(a(n), n=1..22); # Zerinvary Lajos, Oct 07 2007

MATHEMATICA

fib[n_]:=If[n==1||n==2, 1, fib[n-1]+fib[n-2]]; a={}; Do[f1=fib[n]; f2=fib[n+1]; f3=fib[n+2]; p=f1*f2*f3; AppendTo[a, p], {n, 1, 20}]; a (* Vladimir Joseph Stephan Orlovsky, Jul 22 2008 *)

Times@@@Partition[Fibonacci[Range[30]], 3, 1] (* Harvey P. Dale, Aug 18 2011 *)

PROG

(PARI) { for (n=1, 200, a=fibonacci(n)*fibonacci(n + 1)*fibonacci(n + 2); write("b065563.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 22 2009

CROSSREFS

Cf. A000045, A001655.

Sequence in context: A071760 A304579 A036752 * A035105 A073969 A295863

Adjacent sequences:  A065560 A065561 A065562 * A065564 A065565 A065566

KEYWORD

nonn,easy

AUTHOR

Len Smiley, Nov 30 2001

EXTENSIONS

Offset changed from 0 to 1 by Harry J. Smith, Oct 22 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 23 01:24 EDT 2018. Contains 316518 sequences. (Running on oeis4.)