OFFSET
0,3
COMMENTS
Convolution of Fibonacci numbers and Lucas numbers.
Central terms of the triangle in A119457 for n>0. - Reinhard Zumkeller, May 20 2006
d/dx(1 + x + 2x^2 + 3x^3 + 5x^4 + 8x^5 + ...) = (1 + 4x + 9x^2 + ...). - Gary W. Adamson, Jun 27 2009
For n > 0: sums of rows of the triangle in A108035. - Reinhard Zumkeller, Oct 08 2012
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
M. Griffiths, A Restricted Random Walk defined via a Fibonacci Process, Journal of Integer Sequences, Vol. 14 (2011), #11.5.4.
Milan Janjic, Hessenberg Matrices and Integer Sequences , J. Int. Seq. 13 (2010) # 10.7.8, section 3.
Index entries for linear recurrences with constant coefficients, signature (2,1,-2,-1).
FORMULA
O.g.f.: x(2x+1)/(1-x-x^2)^2. - Len Smiley, Dec 11 2001
a(n) = n*Sum_{k=0..n} binomial(k,n-k). - Paul Barry, Sep 25 2004
MAPLE
A023607 := proc(n)
n*combinat[fibonacci](n+1) ;
end proc:
seq(A023607(n), n=0..10) ; # R. J. Mathar, Jul 15 2017
MATHEMATICA
Times@@@Thread[{Range[0, 50], Fibonacci[Range[51]]}] (* Harvey P. Dale, Mar 08 2011 *)
Table[n*Fibonacci[n + 1], {n, 0, 50}]
PROG
(Haskell)
a023607 n = a023607_list !! n
a023607_list = zipWith (*) [0..] $ tail a000045_list
-- Reinhard Zumkeller, Oct 08 2012
(PARI) a(n)=n*fibonacci(n+1) \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Simpler description from Samuel Lachterman (slachterman(AT)fuse.net), Sep 19 2003
Name improved by T. D. Noe, Mar 08 2011
STATUS
approved