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.
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
V. E. Hoggatt and D. A. Lind, The Heights of Fibonacci Polynomials and an Associated Function, Fibonacci Quarterly, Vol. 5, No. 2 (April, 1967), pp. 141-152.
Joseph S. Ozbolt, A New Sequence Derived From a Combination of Cubes with Volume Fn^3, Fibonacci Quarterly, Vol. 50, No. 1 (2012), pp. 19-26.
Index entries for linear recurrences with constant coefficients, signature (3,6,-3,-1).
FORMULA
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
Sum_{n>=1} (-1)^(n+1)/a(n) = A079586 - 3. - Amiram Eldar, Oct 04 2020
Sum_{n>=1} 1/a(n) = A324007. - Amiram Eldar, Feb 09 2023
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
Times@@@Partition[Fibonacci[Range[30]], 3, 1] (* Harvey P. Dale, Aug 18 2011 *)
PROG
(PARI) a(n) = { fibonacci(n)*fibonacci(n + 1)*fibonacci(n + 2) } \\ Harry J. Smith, Oct 22 2009
(Magma) [&*[Fibonacci(n+k): k in [0..2] ]: n in [1..30]]; // Vincenzo Librandi, Apr 09 2020
CROSSREFS
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